Journal articles: 'Doppler redshift'

1

Sandhu, Gurcharn S. "Distinct Doppler Effects for Spontaneously Emitted Photons and Continuously Emitted Waves." Applied Physics Research 9, no. 4 (July 26, 2017): 44. http://dx.doi.org/10.5539/apr.v9n4p44.

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In this paper, we distinguish between the Doppler effects for spontaneously emitted photons and continuously emitted waves. Under certain plausible assumptions, electron orbits can be modeled for simple atomic systems and such studies show that all permissible electron trajectories correspond to elliptical orbits. From the conservation of energy, momentum and angular momentum, in conjunction with the geometrical model of electron orbits, we derive the Doppler effect for spontaneously emitted photons that is quite different from the one used for continuously generated waves. All astronomical redshifts are currently interpreted by assuming the incoming radiation to be continuously emitted waves. Therefore, widely-observed redshift in radiation from most astronomical sources is interpreted to imply the expanding universe, along with cosmological expansion of space. However, for the spontaneously emitted photons, we show that the photons emitted in forward direction parallel to the emitter velocity get redshifted. That means, the astronomical redshift implies that the emission sources are moving towards the observer and our universe is not expanding. All high redshift astronomical objects are likely to be physically disrupted through dynamic instabilities or explosions and their high redshifts are associated with relativistic shock waves propagating towards the observer. Hence the proposed Doppler effect for the spontaneously emitted photons dismisses the cosmological expansion of space and supports a steady state universe.

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Zakir, Zahid. "Slowing time cosmology with initial violetshift and three types of redshift." QUANTUM AND GRAVITATIONAL PHYSICS 2 (August 16, 2021): 1–20. http://dx.doi.org/10.9751/qgph.2-012.7533.

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In general relativity, the stretching of the wavelengths of photons in the expanding universe occurs along the path and does not depend on the velocity of the source. Therefore, the photons from the sources at rest relative to us did not have, and from the sources comoving the expansion there was an initial Doppler redshift, and then on the way both photon fluxes acquired a stretching redshift. As the result, the redshift of the comoving the expansion sources should be at least doubled. But observations show a single redshift already in the linear part, and therefore in cosmological models only with redshifts (Friedmann's and others) there was the double redshift problem with one hundred percent discrepancy between theory and observations. The observational fact of single redshifts means that the photons should have an initial violetshift, which was compensated for along the way by one of two types of redshift. In the model of slowing time cosmology (STC) proposed in 2020, the rate of proper times was higher in earlier epochs, which led to the violetshift, compensated along the way by the stretching redshift. As a result, in STC the observed shift is reduced to the initial Doppler redshift, to which the gravitational redshift is added for distant objects. The relativistic aberration then leads to dimming of the apparent luminosities. The basic relations of STC are presented, including the “distance modulus – redshift”, which are consistent with observations at new values of cosmological parameters. Evolution in early epochs and its influence on the properties of CMB are also discussed. In STC the light velocity was higher in the past and for this reason it has no previously known cosmological problems.

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Zakir, Zahid. "Slowing time cosmology with initial violetshift and three types of redshift." QUANTUM AND GRAVITATIONAL PHYSICS 2 (August 16, 2021): 1–20. http://dx.doi.org/10.9751/qgph.2-012.7133.

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In general relativity, the stretching of the wavelengths of photons in the expanding universe occurs along the path and does not depend on the velocity of the source. Therefore, the photons from the sources at rest relative to us did not have, and from the sources comoving the expansion there was an initial Doppler redshift, and then on the way both photon fluxes acquired a stretching redshift. As the result, the redshift of the comoving the expansion sources should be at least doubled. But observations show a single redshift already in the linear part, and therefore in cosmological models only with redshifts (Friedmann's and others) there was the double redshift problem with one hundred percent discrepancy between theory and observations. The observational fact of single redshifts means that the photons should have an initial violetshift, which was compensated for along the way by one of two types of redshift. In the model of slowing time cosmology (STC) proposed in 2020, the rate of proper times was higher in earlier epochs, which led to the violetshift, compensated along the way by the stretching redshift. As a result, in STC the observed shift is reduced to the initial Doppler redshift, to which the gravitational redshift is added for distant objects. The relativistic aberration then leads to dimming of the apparent luminosities. The basic relations of STC are presented, including the “distance modulus – redshift”, which are consistent with observations at new values of cosmological parameters. Evolution in early epochs and its influence on the properties of CMB are also discussed. In STC the light velocity was higher in the past and for this reason it has no previously known cosmological problems.

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4

Ning, Shou-Li, and LiXin Xu. "The effect of redshift degeneracy and the damping effect of viscous medium on the information extracted from gravitational wave signals." Monthly Notices of the Royal Astronomical Society 500, no. 3 (November 20, 2020): 3999–4003. http://dx.doi.org/10.1093/mnras/staa3592.

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ABSTRACT Considering the cosmological redshift zc, the mass of GW source extracted from GW signal is 1 + zc times larger than its intrinsic value, and distance between detector and GW source should be regarded as luminosity distance. However, besides cosmological redshift, there are other kinds of redshifts should be considered, which is actually ignored, in the analysis of GW data, such as Doppler redshift and gravitational redshift, so the parameters extracted from GW may deviate from their intrinsic values. Another factor that may affect GW is the viscous medium in propagation path of GW, which may damp the GW with a damping rate of 16πGη. Some studies indicate dark matter may interact with each other, thus dark matter may be the origin of viscosity of cosmic medium. Then the GW may be rapidly damped by the viscous medium that is made of dark matter, such as dark matter ‘mini-spike’ around intermediate-mass black hole. In this article, we mainly discuss how Doppler and gravitational redshift, together with the damping effect of viscous medium, affect the informations, such as the mass and redshift of GW source, extracted from GW signals.

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5

Marmet, Paul. "A New Non-Doppler Redshift." Physics Essays 1, no. 1 (March 1, 1988): 24–32. http://dx.doi.org/10.4006/1.3033412.

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6

Kiang, T. "Doppler and cosmological interpretations of redshift." Chinese Astronomy and Astrophysics 25, no. 2 (April 2001): 141–46. http://dx.doi.org/10.1016/s0275-1062(01)00054-6.

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7

Abdelali, Mohamed Lamine, and Noureddine Mebarki. "Redshift effect implications on revised models of Stephan’s Quintet." Modern Physics Letters A 35, no. 01 (September 17, 2019): 1950342. http://dx.doi.org/10.1142/s0217732319503425.

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Recent observations of Stephan’s Quintet (SQ) gave new indications on its formation scenario. Older formation and role of NCG 7317 should be considered in revised numerical models of the compact group. Velocities of group members to recreate are estimated from redshift measurements. Several effects contribute to observed redshifts and a new effect is predicted to be the result of the gravitational interaction between photons and constant magnetic fields creating gravitational waves. The energy carried by these waves is manifested as redshifts of the photons. Cosmological simulation data are used to prove the significant contribution of our effect. The analysis of synthetic observations created from those simulations has shown that redshifts of SQ members could be misinterpreted as caused only from Doppler Effect. The revised models of the group should consider a new method to recreate the formation scenario based on redshift patterns and not mis-estimated velocities.

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8

Hossen, Md Rasel, Sonia Akter Ema, Krzysztof Bolejko, and Geraint F. Lewis. "Mapping the cosmic mass distribution with stacked weak gravitational lensing and Doppler lensing." Monthly Notices of the Royal Astronomical Society 509, no. 4 (November 12, 2021): 5142–54. http://dx.doi.org/10.1093/mnras/stab3292.

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ABSTRACT Dark matter haloes represent the highest density peaks in the matter distribution. Conversely, cosmic voids are underdense patches of the universe. Probing the mass distribution of the universe requires various approaches, including weak gravitational lensing that subtly modifies the shape of distant sources, and Doppler lensing that changes the apparent size and magnitude of objects due to peculiar velocities. In this work, we adopt both gravitational and Doppler lensing effects to study the underlying matter distribution in and around cosmic voids or haloes. We use the relativistic N-body code gevolution, to generate the mass perturbations and develop a new ray-tracing code that relies on the design of the ray bundle method. We consider three categories of halo masses and void radii, and extract the cosmological information by stacking weak-lensing and Doppler lensing signals around voids or haloes. The results of this paper show that the most optimal strategy that combines both gravitational and Doppler lensing effects to map the mass distribution should focus on the redshift range z ≈ 0.3−0.4. The recommendation of this paper is that future spectroscopic surveys should focus on these redshifts and utilize the gravitational and Doppler lensing techniques to extract information about underlying matter distribution across the cosmic web, especially inside cosmic voids. This could provide a complimentary cosmological analysis for ongoing or future low-redshift spectroscopic surveys.

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9

Gentry, Robert V. "A New Redshift Interpretation." Modern Physics Letters A 12, no. 37 (December 7, 1997): 2919–25. http://dx.doi.org/10.1142/s0217732397003034.

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A nonhomogeneous universe with vacuum energy, but without space–time expansion, is utilized together with gravitational and Doppler redshifts as the basis for proposing a new interpretation of the Hubble relation and the 2.7 K Cosmic Blackbody Radiation.

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10

Tifft, W. G., and W. J. Cocke. "Properties of the Redshift." International Astronomical Union Colloquium 124 (1990): 479–83. http://dx.doi.org/10.1017/s0252921100005546.

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Central to any analysis of dynamical systems, or large scale motion, is the interpretation of redshifts of galaxies as classical Doppler velocity shifts. This is a testable assumption and for many years evidence has accumulated that is inconsistent with the assumption. Here we review recent evidence suggesting systematic radial dependence and temporal variation of redshifts.

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11

Pérez, José-Philippe. "Redshift formulas and the Doppler–Fizeau effect." European Journal of Physics 37, no. 1 (November 30, 2015): 015604. http://dx.doi.org/10.1088/0143-0807/37/1/015604.

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12

Marmet, P. "Non-Doppler redshift of some galactic objects." IEEE Transactions on Plasma Science 18, no. 1 (1990): 56–60. http://dx.doi.org/10.1109/27.45504.

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13

Andrianomena, Sambatra, Camille Bonvin, David Bacon, Philip Bull, Chris Clarkson, Roy Maartens, and Teboho Moloi. "Testing general relativity with the Doppler magnification effect." Monthly Notices of the Royal Astronomical Society 488, no. 3 (July 10, 2019): 3759–71. http://dx.doi.org/10.1093/mnras/stz1905.

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ABSTRACT The apparent sizes and brightnesses of galaxies are correlated in a dipolar pattern around matter overdensities in redshift space, appearing larger on their near side and smaller on their far side. The opposite effect occurs for galaxies around an underdense region. These patterns of apparent magnification induce dipole and higher multipole terms in the cross-correlation of galaxy number density fluctuations with galaxy size/brightness (which is sensitive to the convergence field). This provides a means of directly measuring peculiar velocity statistics at low and intermediate redshift, with several advantages for performing cosmological tests of general relativity (GR). In particular, it does not depend on empirically calibrated scaling relations like the Tully–Fisher and Fundamental Plane methods. We show that the next generation of spectroscopic galaxy redshift surveys will be able to measure the Doppler magnification effect with sufficient signal-to-noise ratio to test GR on large scales. We illustrate this with forecasts for the constraints that can be achieved on parametrized deviations from GR for forthcoming low-redshift galaxy surveys with DESI and SKA2. Although the cross-correlation statistic considered has a lower signal-to-noise ratio than RSD, it will be a useful probe of GR since it is sensitive to different systematics.

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14

Qin, Yi-Ping, Hong-Tao Liu, En-Wei Liang, Yun-Ming Dong, and Cheng-Yue Su. "Distribution of the extensive Doppler redshift of quasars." Monthly Notices of the Royal Astronomical Society 351, no. 4 (July 2004): 1319–26. http://dx.doi.org/10.1111/j.1365-2966.2004.07875.x.

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15

Byrd, Gene G., and Mauri J. Valtonen. "Redshift Asymmetries and the Missing Mass." Symposium - International Astronomical Union 124 (1987): 503–6. http://dx.doi.org/10.1017/s0074180900159455.

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We study the existence of missing mass in the outermost regions of galaxies not accessible to study by rotation curve methods. We consider binary galaxies, groups and clusters of galaxies. Arp has previously explained redshift asymmetries in pairs or groups with “non-Doppler redshifts”. Instead, we propose the asymmetries indicate contamination by optical pairs or by members which are not gravitationally bound to the group or pair. The group samples which are commonly used to justify very high missing mass values in spiral galaxies (>> the mass detected by rotation curves) also exhibit significant redshift asymmetries. From this and other information, we conclude that spiral galaxies do not possess very massive halos. Only the rare giant elliptical galaxies, such as the binary pair in the center of the Coma Cluster of galaxies, apparently possess extremely massive halos. Dynamical effects of such giants lead to overestimates of the mass of clusters. The evidence indicates that missing mass sufficient to close the universe is not concentrated in individual galaxies, groups or rich clusters.

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16

CARLIP, S., and R. SCRANTON. "REMARKS ON THE "NEW REDSHIFT INTERPRETATION"." Modern Physics Letters A 14, no. 01 (January 10, 1999): 71–80. http://dx.doi.org/10.1142/s0217732399000109.

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In a recent article,1 Gentry proposed a new static cosmological model that seeks to explain the Hubble relation as a combination of gravitational and Doppler redshifts. We show that Gentry's model, although supposedly based on general relativity, is inconsistent with the Einstein field equations: (a) it requires delicate fine tuning of initial conditions; (b) it is highly unstable, both gravitationally and thermodynamically; and (c) its predictions disagree clearly with observation.

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17

Fernandez, M. A., Simeon Bird, and Phoebe Upton Sanderbeck. "Effect of separate initial conditions on the lyman-α forest in simulations." Monthly Notices of the Royal Astronomical Society 503, no. 2 (February 26, 2021): 1668–79. http://dx.doi.org/10.1093/mnras/stab555.

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ABSTRACT Using a set of high resolution simulations, we quantify the effect of species-specific initial transfer functions on probes of the intergalactic medium (IGM) via the Lyman-α forest. We focus on redshifts 2–6, after H i reionization. We explore the effect of these initial conditions on measures of the thermal state of the low density IGM: the curvature, Doppler width cutoff, and Doppler width distribution. We also examine the matter and flux power spectrum, and potential consequences for constraints on warm dark matter models. We find that the curvature statistic is at most affected at the $\approx 2{{\ \rm per\ cent}}$ level at z = 6. The Doppler width cutoff parameters are affected by $\approx 5{{\ \rm per\ cent}}$ for the intercept, and $\approx 8{{\ \rm per\ cent}}$ for the fit slope, though this is subdominant to sample variation. The Doppler width distribution shows a $\approx 30{{\ \rm per\ cent}}$ effect at z = 3, however the distribution is not fully converged with simulation box size and resolution. The flux power spectrum is at most affected by $\approx 5{{\ \rm per\ cent}}$ at high redshift and small scales. We discuss numerical convergence with simulation parameters.

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18

Fleckinger, Robert. "Comment on ‘Redshift formulas and the Doppler–Fizeau effect’." European Journal of Physics 37, no. 4 (May 24, 2016): 048001. http://dx.doi.org/10.1088/0143-0807/37/4/048001.

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19

Chodorowski, Michał J. "Cosmology Under Milne's Shadow." Publications of the Astronomical Society of Australia 22, no. 3 (2005): 287–91. http://dx.doi.org/10.1071/as05016.

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AbstractBased on the magnitude–redshift diagram for the sample of supernovae Ia analyzed by Perlmutter et al. (1999), Davis & Lineweaver (2004) ruled out the special relativistic interpretation of cosmological redshifts at a confidence level of 23σ. Here, we critically reassess this result. Special relativity is known to describe the dynamics of an empty universe, by means of the Milne kinematic model. Applying only special relativistic concepts, we derive the angular diameter distance and the luminosity distance in the Milne model. In particular, in this model we do not use the underlying metric in its Robertson–Walker form, so our exposition is useful for readers without any knowledge of general relativity. We do however, explicitly use the special relativistic Doppler formula for redshift. We apply the derived luminosity distance to the magnitude–redshift diagram for supernovae Ia of Perlmutter et al. (1999) and show that special relativity fits the data much better than that claimed by Davis & Lineweaver. Specifically, using these data alone, the Milne model is ruled out only at a 2σ level. Alhough not a viable cosmological model, in the context of current research on supernovae Ia it remains a useful reference model when comparing predictions of various cosmological models.

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20

Saga, Shohei, Atsushi Taruya, Michel-Andrès Breton, and Yann Rasera. "Modelling the asymmetry of the halo cross-correlation function with relativistic effects at quasi-linear scales." Monthly Notices of the Royal Astronomical Society 498, no. 1 (August 6, 2020): 981–1001. http://dx.doi.org/10.1093/mnras/staa2232.

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ABSTRACT The observed galaxy distribution via galaxy redshift surveys appears distorted due to redshift-space distortions (RSD). While one dominant contribution to RSD comes from the Doppler effect induced by the peculiar velocity of galaxies, the relativistic effects, including the gravitational redshift effect, are recently recognized to give small but important contributions. Such contributions lead to an asymmetric galaxy clustering along the line of sight, and produce non-vanishing odd multipoles when cross-correlating between different biased objects. However, non-zero odd multipoles are also generated by the Doppler effect beyond the distant-observer approximation, known as the wide-angle effect, and at quasi-linear scales, the interplay between wide-angle and relativistic effects becomes significant. In this paper, based on the formalism developed by Taruya et al., we present a quasi-linear model of the cross-correlation function taking a proper account of both the wide-angle and gravitational redshift effects, as one of the major relativistic effects. Our quasi-linear predictions of the dipole agree well with simulations even at the scales below $20\, h^{-1}\,$Mpc, where non-perturbative contributions from the halo potential play an important role, flipping the sign of the dipole amplitude. When increasing the bias difference and redshift, the scale where the sign flip happens is shifted to a larger scale. We derive a simple approximate formula to quantitatively account for the behaviours of the sign flip.

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Zhang, Yingkang, Tao An, Sándor Frey, Krisztina Éva Gabányi, and Yulia Sotnikova. "Radio Jet Proper-motion Analysis of Nine Distant Quasars above Redshift 3.5." Astrophysical Journal 937, no. 1 (September 1, 2022): 19. http://dx.doi.org/10.3847/1538-4357/ac87f8.

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Abstract Up to now, jet kinematic studies of radio quasars have barely reached beyond the redshift range z > 3.5. This significantly limits our knowledge of high-redshift jets, which can provide key information for understanding the jet nature and the growth of black holes in the early universe. In this paper, we selected nine radio-loud quasars at z > 3.5 which display milliarcsecond-scale jet morphology. We provided evidence of the source nature by presenting high-resolution very long baseline interferometry (VLBI) images of the sample at 8.4 GHz frequency and making spectral index maps. We also consider Gaia optical positions that are available for seven out of the nine quasars for better identification of the jet components within the radio structures. We find that six sources can be classified as core–jet blazars. The remaining three objects are more likely young jetted radio sources, compact symmetric objects. By including multiepoch archival VLBI data, we also obtained jet component proper motions of the sample and estimated the jet kinematic and geometric parameters (Doppler factor, Lorentz factor, and viewing angle). Our results show that at z > 3.5, the jet’s apparent transverse speeds do not exceed 20 times the speed of light (c). This is consistent with earlier high-redshift quasar measurements in the literature and the tendency derived from low-redshift blazars that fast jet speeds (>40c) only occur at low redshifts. The results from this paper contribute to the understanding of the cosmological evolution of radio active galactic nuclei.

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22

Tabirian, Levon N. "Addressing redshift controversies through the doppler analog of spectral redshifts caused by light deceleration in dynamic media." Optik 183 (April 2019): 723–26. http://dx.doi.org/10.1016/j.ijleo.2019.02.150.

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23

Loeb, Abraham. "Gravitational Redshift for Wide Binaries in Gaia eDR3." Research Notes of the AAS 6, no. 3 (March 22, 2022): 55. http://dx.doi.org/10.3847/2515-5172/ac5ea9.

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Abstract The Doppler effect is commonly used to infer the velocity difference between stars based on the relative shifts in the rest-frame wavelengths of their spectral features. In wide binaries, the difference in gravitational redshift from the surfaces of the constituent stars with distinct compactness dominates at separations ≳10−2 pc. I suggest that this effect became apparent for wide pairs in the Gaia eDR3 catalog but was incorrectly interpreted as a possible modification of Newtonian gravity in the internal kinematics of very wide binaries.

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SIMIĆ, S., and L. Č. POPOVIĆ. "INVESTIGATION OF ELEMENT ABUNDANCES IN THE SURROUNDINGS OF GRB AFTERGLOWS." International Journal of Modern Physics D 17, no. 09 (September 2008): 1377–82. http://dx.doi.org/10.1142/s0218271808012942.

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In the case of high energy collimated outflows it is important to know the density and structure of material through which jets propagate. Here we present a simple study of the environment of GRBs where the relativistic ejecta travel during the event. We use observed spectral lines in the afterglow of gamma-ray bursts and by constructing the curve of growth for most redshifted lines, we extract the column densities and Doppler parameter. This can give us the overall picture of abundances in the vicinity of GRBs. Also, we compare this result with the spectral lines with lower redshift to examine the dependence of elemental abundances on the distance from GRB event.

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25

Schroeder, Paul. "Doppler and an End of Expansion." Energy and Earth Science 4, no. 1 (March 9, 2021): p14. http://dx.doi.org/10.22158/ees.v4n1p14.

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The concept today is that our universe is in a state of expansion as everything is moving away from us, and away from everywhere. This idea is specifically a conclusion to the finding of the frequency of the waves of light from the source being distorted, theoretically by the motion of the source relative to the observer. The frequency variation is called Doppler which was originally assigned to distorted sound from arriving trains. This is an analysis of Doppler theory that revels that a redshift of star light beams occur when the stars are “revolving” relative to an observer (such as us on earth). Everything in space does revolve around an observer. Think about this!

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Cipparrone, G., D. Duca, C. Umeton, and N. V. Tabiryan. "Observation of Doppler-like redshift due to light interaction with matter." Physical Review Letters 71, no. 24 (December 13, 1993): 3955–58. http://dx.doi.org/10.1103/physrevlett.71.3955.

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27

Farley, Francis J. M. "Does gravity operate between galaxies? Observational evidence re-examined." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, no. 2122 (May 19, 2010): 3089–96. http://dx.doi.org/10.1098/rspa.2010.0044.

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The redshifts and luminosities of type 1A supernovae are conventionally fitted with the current paradigm, which holds that the galaxies are locally stationary in an expanding metric. The fit fails unless the expansion is accelerating; driven perhaps by ‘dark energy’. Is the recession of the galaxies slowed down by gravity or speeded up by some repulsive force? To shed light on this question the redshifts and apparent magnitudes of type 1A supernovae are re-analysed in a cartesian frame of reference omitting gravitational effects. The redshift is ascribed to the relativistic Doppler effect which gives the recession velocity when the light was emitted; if this has not changed, the distance reached and the luminosity follow immediately. This simple concept fits the observations surprisingly well with the Hubble constant H 0 =62.9±0.3 km s −1 Mpc −1 . It appears that the galaxies recede at unchanging velocities, so on the largest scale there is no significant intergalactic force. Reasons for the apparent absence of an intergalactic force are discussed.

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Lu, L. ‐Z, Y. ‐P Qin, and A. C. Gupta. "A Subset of Quasars Identified by Large Values of Their Doppler Redshift." Astrophysical Journal 669, no. 1 (November 2007): 74–84. http://dx.doi.org/10.1086/521324.

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29

Levenspiel, Octave. "The age of our universe." Chemical Industry 62, no. 5 (2008): 313–16. http://dx.doi.org/10.2298/hemind0805313l.

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If we assume that the observed Redshift of starlight is due to the Doppler effect we end up with models of the universe which contradict the basic laws of science. If we assume that the red shift may be due to a tiring of light, an assumption still to be tested, we end up with no contradiction with the laws of science. You the reader must choose.

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Romano, Antonio Enea. "Hubble trouble or Hubble bubble?" International Journal of Modern Physics D 27, no. 09 (July 2018): 1850102. http://dx.doi.org/10.1142/s021827181850102x.

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The recent analysis of low-redshift supernovae (SN) has increased the apparent tension between the value of [Formula: see text] estimated from low and high redshift observations such as the cosmic microwave background (CMB) radiation. At the same time other observations have provided evidence of the existence of local radial inhomogeneities extending in different directions up to a redshift of about [Formula: see text]. About [Formula: see text] of the Cepheids used for SN calibration are directly affected because they are located along the directions of these inhomogeneities. We compute with different methods the effects of these inhomogeneities on the low-redshift luminosity and angular diameter distance using an exact solution of the Einstein’s equations, linear perturbation theory and a low-redshift expansion. We confirm that at low redshift the dominant effect is the nonrelativistic Doppler redshift correction, which is proportional to the volume averaged density contrast and to the comoving distance from the center. We derive a new simple formula relating directly the luminosity distance to the monopole of the density contrast, which does not involve any metric perturbation. We then use it to develop a new inversion method to reconstruct the monopole of the density field from the deviations of the redshift uncorrected observed luminosity distance respect to the [Formula: see text]CDM prediction based on cosmological parameters obtained from large scale observations. The inversion method confirms the existence of inhomogeneities whose effects were not previously taken into account because the [Formula: see text] [G. Lavaux and M. J. Hudson, Mon. Not. R. Astron. Soc. 416 (2011) 2840] density field maps used to obtain the peculiar velocity [J. Carrick et al., Mon. Not. R. Astron. Soc. 450 (2015) 317] for redshift correction were for [Formula: see text], which is not a sufficiently large scale to detect the presence of inhomogeneities extending up to [Formula: see text]. The inhomogeneity does not affect the high redshift luminosity distance because the volume averaged density contrast tends to zero asymptotically, making the value of [Formula: see text] obtained from CMB observations insensitive to any local structure. The inversion method can provide a unique tool to reconstruct the density field at high redshift where only SN data is available, and in particular to normalize correctly the density field respect to the average large scale density of the Universe.

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31

Pasquini, L., A. F. Pala, H. G. Ludwig, I. C. Lẽao, J. R. de Medeiros, and A. Weiss. "Masses of the Hyades white dwarfs." Astronomy & Astrophysics 627 (July 2019): L8. http://dx.doi.org/10.1051/0004-6361/201935835.

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Context. It is possible to accurately measure the masses of the white dwarfs (WDs) in the Hyades cluster using gravitational redshift, because the radial velocity of the stars can be obtained independently of spectroscopy from astrometry and the cluster has a low velocity dispersion. Aims. We aim to obtain an accurate measurement of the Hyades WD masses by determining the mass-to-radius ratio (M/R) from the observed gravitational redshift, and to compare them with masses derived from other methods. Methods. We analyse archive high-resolution UVES-VLT spectra of six WDs belonging to the Hyades to measure their Doppler shift, from which M/R is determined after subtracting the astrometric radial velocity. We estimate the radii using Gaia photometry as well as literature data. Results. The M/R error associated to the gravitational redshift measurement is about 5%. The radii estimates, evaluated with different methods, are in very good agreement, though they can differ by up to 4% depending on the quality of the data. The masses based on gravitational redshift are systematically smaller than those derived from other methods, by a minimum of ∼0.02 up to 0.05 solar masses. While this difference is within our measurement uncertainty, the fact that it is systematic indicates a likely real discrepancy between the different methods. Conclusions. We show that the M/R derived from gravitational redshift measurements is a powerful tool to determine the masses of the Hyades WDs and could reveal interesting properties of their atmospheres. The technique can be improved by using dedicated spectrographs, and can be extended to other clusters, making it unique in its ability to accurately and empirically determine the masses of WDs in open clusters. At the same time we prove that gravitational redshift in WDs agrees with the predictions of stellar evolution models to within a few percent.

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Viljoen, Jan-Albert, José Fonseca, and Roy Maartens. "Multi-wavelength spectroscopic probes: prospects for primordial non-Gaussianity and relativistic effects." Journal of Cosmology and Astroparticle Physics 2021, no. 11 (November 1, 2021): 010. http://dx.doi.org/10.1088/1475-7516/2021/11/010.

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Abstract Next-generation cosmological surveys will observe larger cosmic volumes than ever before, enabling us to access information on the primordial Universe, as well as on relativistic effects. We consider forthcoming 21cm intensity mapping surveys (SKAO) and optical galaxy surveys (DESI and Euclid), combining the information via multi-tracer cross-correlations that suppress cosmic variance on ultra-large scales. In order to fully incorporate wide-angle effects and redshift-bin cross-correlations, together with lensing magnification and other relativistic effects, we use the angular power spectra, Cℓ (zi ,zj ). Applying a Fisher analysis, we forecast the expected precision on f NL and the detectability of lensing and other relativistic effects. We find that the full combination of two pairs of 21cm and galaxy surveys, one pair at low redshift and one at high redshift, could deliver σ(f NL) ∼ 1.5, detect the Doppler effect with a signal-to-noise ratio ∼8 and measure the lensing convergence contribution at ∼2% precision. In a companion paper, we show that the best-fit values of f NL and of standard cosmological parameters are significantly biased if the lensing contribution neglected.

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Sahakyan, N., D. Israyelyan, G. Harutyunyan, M. Khachatryan, and S. Gasparyan. "Multiwavelength study of high-redshift blazars." Monthly Notices of the Royal Astronomical Society 498, no. 2 (August 17, 2020): 2594–613. http://dx.doi.org/10.1093/mnras/staa2477.

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ABSTRACT High-redshift blazars are among the most powerful objects in the Universe. The spectral and temporal properties of 33 distant blazars (z > 2.5) detected in the high-energy γ-ray band are investigated by analysing the Fermi-LAT and Swift Ultraviolet and Optical Telescope/X-ray Telescope (UVOT/XRT) data. The considered sources have soft time-averaged γ-ray spectra (Γγ ≥ 2.2) whereas those that have been observed in the X-ray band have hard X-ray spectra (ΓX = 1.01−1.86). The γ-ray flux of high-redshift blazars ranges from 4.84 × 10−10 to 1.50 × 10−7 photon cm−2 s−1 and the luminosity is within (0.10−5.54) × 1048 erg s−1 which during the γ-ray flares increases up to (0.1−1) × 1050 erg s−1. In the X-ray band, only the emission of PKS 0438−43, B2 0743+25, and TXS 0222+185 is found to vary in different Swift XRT observations whereas in the γ-ray band, the emission is variable for fourteen sources: the flux of B3 1343+451 and PKS 0537−286 changes in sub-day scales, that of PKS 0347−211 and PKS 0451−28 in day scales, while the γ-ray variability of the others is in week or month scales. The properties of distant blazar jets are derived by modelling the multiwavelength spectral energy distributions within a one-zone leptonic scenario assuming that the X-ray and γ-ray emissions are produced from inverse Compton scattering of synchrotron and dusty torus photons. From the fitting, the emission region size is found to be ≤0.05 pc and the magnetic field and the Doppler factor are correspondingly within 0.10−1.74 G and 10.0−27.4. By modelling the optical–UV excess, we found that the central black hole masses and accretion disc luminosities are within Ld ≃ (1.09−10.94) × 1046 erg s−1 and (1.69−5.35) × 109 M⊙, respectively.

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Zarro, Dominic M., and Richard C. Canfield. "Chromospheric Downflows as a Diagnostic of Solar Flare Heating." International Astronomical Union Colloquium 104, no. 2 (1989): 203–6. http://dx.doi.org/10.1017/s0252921100154168.

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AbstractUsing coordinated X-ray and Hα observations of five solar flares, we investigate the dynamics of chromospheric condensations formed during chromospheric evaporation. We show that the peak downflow velocity of condensations predicted by simple hydrodynamic compression of the chromosphere is in good agreement with empirical downflow velocities implied by impulsive phase Hα redwing Doppler shifts. This agreement indicates that the Hα wing redshift provides a useful diagnostic of the pressure excess in the evaporating region and, hence, the energy flux driving chromospheric evaporation.

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Schwartz, D. A., H. L. Marshall, D. M. Worrall, M. Birkinshaw, E. Perlman, J. E. J. Lovell, D. Jauncey, et al. "A survey of X-ray emission from 100 kpc radio jets." Proceedings of the International Astronomical Union 10, S313 (September 2014): 219–24. http://dx.doi.org/10.1017/s1743921315002215.

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AbstractWe have completed a Chandra snapshot survey of 54 radio jets that are extended on arcsec scales. These are associated with flat spectrum radio quasars spanning a redshift range z=0.3 to 2.1. X-ray emission is detected from the jet of approximately 60% of the sample objects. We assume minimum energy and apply conditions consistent with the original Felten-Morrison calculations in order to estimate the Lorentz factors and the apparent Doppler factors. This allows estimates of the enthalpy fluxes, which turn out to be comparable to the radiative luminosities.

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Loeb, Abraham. "Spurious Radial Migration from Relativistic Effects in the Milky Way Disk." Research Notes of the AAS 6, no. 4 (April 11, 2022): 72. http://dx.doi.org/10.3847/2515-5172/ac651f.

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Abstract The gradient of the gravitational redshift in the potential of the Milky Way induces an apparent spurious radial migration. I show that this effect is simply related to the local acceleration, which was measured recently by Gaia eDR3, implying a spectroscopic shift of −2.4 × 10−2(r/8 kpc)−1 km s−1 kpc−1. The transverse Doppler effect yields a comparable contribution. The spurious radial velocity from both relativistic effects amounts to crossing a major portion of the Milky Way disk during the age of the universe, and must be corrected for in any future measurement of the actual radial migration of stars.

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Woerd, H. van der, N. E. White, and S. M. Kahn. "X-ray Spectroscopy of the Ultra-soft Transient 4U1543-47." International Astronomical Union Colloquium 115 (1990): 205–8. http://dx.doi.org/10.1017/s0252921100012355.

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AbstractThe X-ray transient 4U1543-47 was observed in 1983 by the EXOSAT observatory near the maximum of an outburst. The X-ray spectrum was measured using a gas scintillation proportional counter (GSPC) and a transmission grating spectrometer (TGS). Two emission line features are resolved. A broad (FWHM ~2.7 keV) line at 5.9 keV is detected in the GSPC, which we interprete as a redshifted and broadened iron Kα line. The Une broadening and redshift may arise from either Compton scattering in a cool plasma with small optical depth (τ ≈ 5), or from Doppler and relativistic effects in the vicinity of a compact object. The spectrum below 2 keV, obtained with the TGS, shows evidence for a broad emission line feature at 0.74 keV, which may be an iron L-transition complex. However, we find that such an emission feature could be an artifact caused by an anomalously low interstellar absorption by neutral Oxygen. The continuum emission is extremely soft and is well described by an unsaturated Comptonized spectrum from a very cool plasma (kT = 0.84 keV) with large scattering depth (τ ≈ 27). The continuum spectrum is strikingly similar to that of black hole candidate LMC X-3.

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T. H. Wu, Edward. "Redshift Caused by Acceleration Doppler Effect and Hubble’s Law Based on Wu’s Spacetime Accelerating Shrinkage Theory." American Journal of Modern Physics 6, no. 1 (2017): 10. http://dx.doi.org/10.11648/j.ajmp.20170601.12.

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DITTUS, HANSJÖRG, and CLAUS LÄMMERZAHL. "THE CLOCK MISSION OPTIS." International Journal of Modern Physics D 16, no. 12b (December 2007): 2499–510. http://dx.doi.org/10.1142/s0218271807011334.

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Clocks are an almost universal tool for exploring the fundamental structure of theories related to relativity. For future clock experiments, it is important for them to be performed in space. One mission which has the capability to perform and improve all relativity tests based on clocks by several orders of magnitude is OPTIS. These tests consist of (i) tests of the isotropy of light propagation (from which information about the matter sector which the optical resonators are made of can also be drawn), (ii) tests of the constancy of the speed of light, (iii) tests of the universality of the gravitational redshift by comparing clocks based on light propagation, like light clocks and various atomic clocks, (iv) time dilation based on the Doppler effect, (v) measuring the absolute gravitational redshift, (vi) measuring the perihelion advance of the satellite's orbit by using very precise tracking techniques, (vii) measuring the Lense–Thirring effect, and (viii) testing Newton's gravitational potential law on the scale of Earth-bound satellites. The corresponding tests are not only important for fundamental physics but also indispensable for practical purposes like navigation, Earth sciences, metrology, etc.

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Fan, J. H., G. Z. Xie, Y. H. Zhang, and Y. P. Qin. "The Relativistic Beaming Model and Superluminal Motions." International Astronomical Union Colloquium 159 (1997): 74–75. http://dx.doi.org/10.1017/s0252921100039683.

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In this paper, we consider a compilation of 55 objects with known superluminal motions (SM), and whose flux density (X-ray, optical, radio), core dominance parameter (R), superluminal velocity, and radio Doppler factor (δR) are known. Our study shows that SM is consistent with the beaming model, and the relationis reasonable. The statistical correlation between superluminal velocity and redshift is a result of selection and the statistical correlation between R and brightness temperature (Tob) is actually a reflection of the correlations between δ, R, and Tob for objects with SM. Up to now, 59 objects have been reported to have SM, but for reasons discussed elsewhere (Vermeulen & Cohen 1994), only 55 are considered here.

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Namekata, Kosuke, Kiyoshi Ichimoto, Takako T. Ishii, and Kazunari Shibata. "Sun-as-a-star Analysis of Hα Spectra of a Solar Flare Observed by SMART/SDDI: Time Evolution of Red Asymmetry and Line Broadening." Astrophysical Journal 933, no. 2 (July 1, 2022): 209. http://dx.doi.org/10.3847/1538-4357/ac75cd.

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Abstract Stellar flares sometimes show red/blue asymmetries of the Hα line, which can indicate chromospheric dynamics and prominence activations. However, the origin of asymmetries is not completely understood. For a deeper understanding of stellar data, we performed a Sun-as-a-star analysis of Hα line profiles of an M4.2-class solar flare showing dominant emissions from flare ribbons by using the data of the Solar Dynamics Doppler Imager on board the Solar Magnetic Activity Research Telescope at the Hida Observatory. Sun-as-a-star Hα spectra of the flare show red asymmetry of up to ∼95 km s−1 and line broadening of up to ∼7.5 Å. The Sun-as-a-star Hα profiles are consistent with spectra from flare regions with weak intensity, but they take smaller redshift velocities and line widths by a factor of ∼2 than those with strong intensity. The redshift velocities, as well as line widths, peak out and decay more rapidly than the Hα equivalent widths, which is consistent with the chromospheric condensation model and spatially resolved flare spectra. This suggests that as a result of superposition, the nature of chromospheric condensation is observable even from stellar flare spectra. The time evolution of redshift velocities is found to be similar to that of luminosities of near-ultraviolet rays (1600 Å), while the time evolution of line broadening is similar to that of optical white lights. These Hα spectral behaviors in Sun-as-a-star view could be helpful to distinguish whether the origin of Hα red asymmetry of stellar flares is a flare ribbon or other phenomena.

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Lister, Matthew L., and Alan P. Marscher. "Statistical Effects of Doppler Beaming and Malmquist Bias on Flux-Limited Samples of Compact Radio Sources." International Astronomical Union Colloquium 164 (1998): 137–38. http://dx.doi.org/10.1017/s0252921100044882.

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AbstractWe examine the effects of Doppler beaming on flux-limited samples of compact extragalactic radio sources using Monte Carlo simulations. We incorporate a luminosity function and z-distribution for the parent population, and investigate models in which the unbeamed synchrotron luminosity L of a relativistic jet is related to its bulk Lorentz factor Γ. The predicted flux density, redshift, monochromatic luminosity, and apparent velocity distributions of our simulated flux-limited samples are compared to the Caltech-Jodrell Bank (CJF) sample of flat-spectrum, radio core-dominated active galactic nuclei (AGNs).We find that a relation between L and Γ is not needed to reproduce the characteristics of the CJF sample. Introducing a positive correlation between these quantities results in an underabundance of objects with high viewing angles, while a negative correlation gives generally poor fits to the data.

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W Hunstead, Richard, and Max Pettini. "The Lyman a Forest in QSOs: A Window on Intergalactic Clouds at High Redshift." Australian Journal of Physics 43, no. 2 (1990): 211. http://dx.doi.org/10.1071/ph900211.

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It is now well established that the number density of Lya forest absorption lines evolves strongly with redshift. When combined with the observed exponential distribution of equivalent widths, this points to a steep dependence of H I column density on z. New information on the nature of the Lya clouds has recently been obtained from high-resolution AAT echelle observations (6.5 km S-l FWHM) of the QSO 2206-199N. Profile fits to unblended Lya lines in the interval Zabs = 2.103 - 2.587 have established a clear trend between the Doppler velocity dispersion b and column density N, suggesting that b is measuring large-scale motions within the Lya clouds rather than their temperatures. If correct, cloud temperatures (set by the lowest b values) are probably < 5000 K instead of the 30000 K usually assumed, implying that the clouds are predominantly neutral. Previous data at lower resolution are shown to be roughly consistent with the new b:N trend, after allowing for the evolutionary dependence of N on z. The new observations are difficult to accommodate within the conventional framework of pressure-confined, low-density, ionised clouds; instead, we suggest that the Lya clouds may be either in the form of dense, thin sheets or may be gravitationally confined.

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Tiwari, Sanjiv K., Viggo H. Hansteen, Bart De Pontieu, Navdeep K. Panesar, and David Berghmans. "SolO/EUI Observations of Ubiquitous Fine-scale Bright Dots in an Emerging Flux Region: Comparison with a Bifrost MHD Simulation." Astrophysical Journal 929, no. 1 (April 1, 2022): 103. http://dx.doi.org/10.3847/1538-4357/ac5d46.

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Abstract We report on the presence of numerous tiny bright dots in and around an emerging flux region (an X-ray/coronal bright point) observed with SolO’s EUI/HRIEUV in 174 Å. These dots are roundish and have a diameter of 675 ± 300 km, a lifetime of 50 ± 35 s, and an intensity enhancement of 30% ± 10% above their immediate surroundings. About half of the dots remain isolated during their evolution and move randomly and slowly (<10 km s−1). The other half show extensions, appearing as a small loop or surge/jet, with intensity propagations below 30 km s−1. Many of the bigger and brighter HRIEUV dots are discernible in the SDO/AIA 171 Å channel, have significant emissivity in the temperature range of 1–2 MK, and are often located at polarity inversion lines observed in SDO/HMI LOS magnetograms. Although not as pervasive as in observations, a Bifrost MHD simulation of an emerging flux region does show dots in synthetic Fe ix/x images. These dots in the simulation show distinct Doppler signatures—blueshifts and redshifts coexist, or a redshift of the order of 10 km s−1 is followed by a blueshift of similar or higher magnitude. The synthetic images of O v/vi and Si iv lines, which represent transition region radiation, also show the dots that are observed in Fe ix/x images, often expanded in size, or extended as a loop, and always with stronger Doppler velocities (up to 100 km s−1) than that in Fe ix/x lines. Our observation and simulation results, together with the field geometry of dots in the simulation, suggest that most dots in emerging flux regions form in the lower solar atmosphere (at ≈ 1 Mm) by magnetic reconnection between emerging and preexisting/emerged magnetic field. Some dots might be manifestations of magnetoacoustic shocks through the line formation region of Fe ix/x emission.

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Frey, Sándor, Zsolt Paragi, Judit O. Fogasy, and Leonid I. Gurvits. "The first estimate of radio jet proper motion at z > 5." Monthly Notices of the Royal Astronomical Society 446, no. 3 (November 29, 2014): 2921–28. http://dx.doi.org/10.1093/mnras/stu2294.

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Abstract The extremely high-redshift (z = 5.3) radio source SDSS J102623.61+254259.5 (J1026+2542) is among the most distant and most luminous radio-loud active galactic nuclei (AGN) known to date. Its one-sided radio jet structure on milliarcsecond (mas) and ∼10-mas scales typical for blazars was first imaged at 5 GHz with very long baseline interferometry (VLBI) in 2006. Here we report on our dual-frequency (1.7 and 5 GHz) imaging observations performed with the European VLBI Network (EVN) in 2013. The prominent jet structure allows us to identify individual components whose apparent displacement can be detected over the time span of 7.33 yr. This is the first time when jet proper motions are directly derived in a blazar at z > 5. The small values of up to ∼0.1 mas yr−1 are consistent with what is expected in a relativistic cosmological model if redshift is a measure of distance. The apparent superluminal jet speeds, considered tentative because derived from two epochs only, exceed 10 c for three different components along the jet. Based on modelling its spectral energy distribution, J1026+2542 is known to have its X-ray jet oriented close to the line of sight, with significant Doppler boosting and a large bulk Lorentz factor (Γ ≈ 13). The new VLBI observations, indicating ∼2.3 × 1012 K lower limit to the core brightness temperature, are consistent with this picture. The spectral index in the core region is −0.35.

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Yaqoob, T., I. M. George, K. Nandra, T. J. Turner, S. Zobair, and P. J. Serlemitsos. "A Highly Doppler Blueshifted F[CLC]e[/CLC]-K Emission Line in the High-Redshift QSO PKS 2149−306." Astrophysical Journal 525, no. 1 (November 1, 1999): L9—L12. http://dx.doi.org/10.1086/312327.

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Miller, Sarah H. "The Dwarfs Beyond: Relating Stellar and Halo Mass in Dwarf Galaxies to z ~ 1." Proceedings of the International Astronomical Union 10, S311 (July 2014): 150–53. http://dx.doi.org/10.1017/s1743921315003579.

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AbstractDo the kinematics and mass profiles of dwarf galaxies present a fundamental challenge to standard cold dark matter (CDM) models? New, deep spectroscopy using DEIMOS on Keck for hundreds of low stellar mass (107-109 M⊙ star-forming galaxies at intermediate redshift (0.2 < z < 1) addresses this inquiry in a way that is less subject to cosmic variance and environmental bias than previous, more local work. Half of this sample reveals resolved, doppler-shifted nebular emission, used to constrain rotation curves. From these we can construct the stellar mass Tully-Fisher relation to masses as low as ~107 M⊙, and a persistent discrepancy is found between predictions from simulations and models compared to our observations. We suggest on-going and future tests that will be more effective in distinguishing between the effects of baryonic feedback and alternative models of dark matter in this remarkable regime.

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Worrall, D. M., M. Birkinshaw, H. L. Marshall, D. A. Schwartz, A. Siemiginowska, and J. F. C. Wardle. "Inverse-Compton scattering in the resolved jet of the high-redshift quasar PKS J1421−0643." Monthly Notices of the Royal Astronomical Society 497, no. 1 (July 8, 2020): 988–1000. http://dx.doi.org/10.1093/mnras/staa1975.

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ABSTRACT Despite the fact that kpc-scale inverse-Compton (iC) scattering of cosmic microwave background (CMB) photons into the X-ray band is mandated, proof of detection in resolved quasar jets is often insecure. High redshift provides favourable conditions due to the increased energy density of the CMB, and it allows constraints to be placed on the radio synchrotron-emitting electron component at high energies that are otherwise inaccessible. We present new X-ray, optical, and radio results from Chandra, HST, and the VLA for the core and resolved jet in the z = 3.69 quasar PKS J1421−0643. The X-ray jet extends for about 4.5 arcsec (32 kpc projected length). The jet’s radio spectrum is abnormally steep and consistent with electrons being accelerated to a maximum Lorentz factor of about 5000. Results argue in favour of the detection of iC X-rays for modest magnetic field strength of a few nT, Doppler factor of about 4, and viewing angle of about 15°, and predict the jet to be largely invisible in most other spectral bands including the far- and mid-infrared and high-energy gamma-ray. The jet power is estimated to be about 3 × 1046 erg s−1 which is of order a tenth of the quasar bolometric power, for an electron–positron jet. The jet radiative power is only about 0.07 per cent of the jet power, with a smaller radiated power ratio if the jet contains heavy particles, so most of the jet power is available for heating the intergalactic medium.

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Maartens, Roy, José Fonseca, Stefano Camera, Sheean Jolicoeur, Jan-Albert Viljoen, and Chris Clarkson. "Magnification and evolution biases in large-scale structure surveys." Journal of Cosmology and Astroparticle Physics 2021, no. 12 (December 1, 2021): 009. http://dx.doi.org/10.1088/1475-7516/2021/12/009.

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Abstract Measurements of galaxy clustering in upcoming surveys such as those planned for the Euclid and Roman satellites, and the SKA Observatory, will be sensitive to distortions from lensing magnification and Doppler effects, beyond the standard redshift-space distortions. The amplitude of these contributions depends sensitively on magnification bias and evolution bias in the galaxy number density. Magnification bias quantifies the change in the observed number of galaxies gained or lost by lensing magnification, while evolution bias quantifies the physical change in the galaxy number density relative to the conserved case. These biases are given by derivatives of the number density, and consequently are very sensitive to the form of the luminosity function. We give a careful derivation of the magnification and evolution biases, clarifying a number of results in the literature. We then examine the biases for a variety of surveys, encompassing galaxy surveys and line intensity mapping at radio and optical/near-infrared wavelengths.

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Riazuelo, Alain. "Seeing relativity-I: Ray tracing in a Schwarzschild metric to explore the maximal analytic extension of the metric and making a proper rendering of the stars." International Journal of Modern Physics D 28, no. 02 (January 2019): 1950042. http://dx.doi.org/10.1142/s0218271819500421.

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We present an implementation of a ray tracing code in the Schwarzschild metric. We aim at building a numerical code with a correct implementation of both special (aberration, amplification and Doppler) and general (deflection of light, lensing and gravitational redshift) relativistic effects so as to simulate what an observer with arbitrary velocity would see near, or possibly within, the black hole. We also pay some specific attention to perform a satisfactory rendering of stars. Using this code, we then show several unexplored features of the maximal analytical extension of the metric. In particular, we study the aspect of the second asymptotic region of the metric as seen by an observer crossing the horizon. We also address several aspects related to the white hole region (i.e. past singularity) seen both from outside the black hole, inside the future horizon and inside the past horizon, which gives rise to the most counter-intuitive effects.

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Journal articles on the topic 'Doppler redshift'

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