Journal articles: 'Einstein constraint system'

1

Druet, Olivier, and Bruno Premoselli. "Stability of the Einstein–Lichnerowicz constraint system." Mathematische Annalen 362, no. 3-4 (November 29, 2014): 839–86. http://dx.doi.org/10.1007/s00208-014-1145-0.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

Premoselli, Bruno. "Stability and Instability of the Einstein–Lichnerowicz Constraint System." International Mathematics Research Notices 2016, no. 7 (June 24, 2015): 1951–2025. http://dx.doi.org/10.1093/imrn/rnv193.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

Premoselli, Bruno. "The Einstein-Scalar Field Constraint System in the Positive Case." Communications in Mathematical Physics 326, no. 2 (November 27, 2013): 543–57. http://dx.doi.org/10.1007/s00220-013-1852-5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

Futamase, T., and T. Hamana. "Constraint on the Cosmological Constant by Einstein Ring System 0047-2808." Progress of Theoretical Physics 102, no. 5 (November 1, 1999): 1037–41. http://dx.doi.org/10.1143/ptp.102.1037.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

Rahaman, Farook, Anirudh Pradhan, Nasr Ahmed, Saibal Ray, Bijan Saha, and Mosiur Rahaman. "Fluid sphere: Stability problem and dimensional constraint." International Journal of Modern Physics D 24, no. 07 (May 27, 2015): 1550049. http://dx.doi.org/10.1142/s0218271815500492.

Full text

Abstract:

We study different dimensional fluids inspired by noncommutative geometry which admit conformal Killing vector (CKV). The solutions of the Einstein field equations were examined specifically for five different set of spacetime. We calculate the active gravitational mass and impose stability conditions of the fluid sphere. The analysis thus carried out immediately indicates that at four dimension only one can get a stable configuration for any spherically symmetric stellar system and any other dimension, lower or higher, becomes untenable as far as the stability of a system is concerned.

APA, Harvard, Vancouver, ISO, and other styles

6

Choquet-Bruhat, Yvonne, James Isenberg, and Daniel Pollack. "The constraint equations for the Einstein-scalar field system on compact manifolds." Classical and Quantum Gravity 24, no. 4 (January 17, 2007): 809–28. http://dx.doi.org/10.1088/0264-9381/24/4/004.

Full text

APA, Harvard, Vancouver, ISO, and other styles

7

Kouneiher, J. "Einstein flow and cosmology." International Journal of Modern Physics A 30, no. 18n19 (July 8, 2015): 1530047. http://dx.doi.org/10.1142/s0217751x15300471.

Full text

Abstract:

The recent evolution of the observational technics and the development of new tools in cosmology and gravitation have a significant impact on the study of the cosmological models. In particular, the qualitative and numerical methods used in dynamical system and elsewhere, enable the resolution of some difficult problems and allow the analysis of different cosmological models even with a limited number of symmetries. On the other hand, following Einstein point of view the manifold [Formula: see text] and the metric should be built simultaneously when solving Einstein’s equation [Formula: see text]. From this point of view, the only kinematic condition imposed is that at each point of space–time, the tangent space is endowed with a metric (which is a Minkowski metric in the physical case of pseudo-Riemannian manifolds and an Euclidean one in the Riemannian analogous problem). Then the field [Formula: see text] describes the way these metrics depend on the point in a smooth way and the Einstein equation is the “dynamical” constraint on [Formula: see text]. So, we have to imagine an infinite continuous family of copies of the same Minkowski or Euclidean space and to find a way to sew together these infinitesimal pieces into a manifold, by respecting Einstein’s equation. Thus, Einstein field equations do not fix once and for all the global topology. [Formula: see text] Given this freedom in the topology of the space–time manifold, a question arises as to how free the choice of these topologies may be and how one may hope to determine them, which in turn is intimately related to the observational consequences of the space–time possessing nontrivial topologies. Therefore, in this paper we will use a different qualitative dynamical methods to determine the actual topology of the space–time.

APA, Harvard, Vancouver, ISO, and other styles

8

Brauer, Uwe, and Lavi Karp. "Well-posedness of the Einstein–Euler system in asymptotically flat spacetimes: The constraint equations." Journal of Differential Equations 251, no. 6 (September 2011): 1428–46. http://dx.doi.org/10.1016/j.jde.2011.05.037.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

He, Q. "An event-mixing method using energy hierarchy constraint for two-pion Bose–Einstein correlations measurements in ππx system." International Journal of Modern Physics E 27, no. 11 (November 2018): 1850095. http://dx.doi.org/10.1142/s0218301318500957.

Full text

Abstract:

For the measurement of two-pion Bose–Einstein correlations (BEC) in reactions with [Formula: see text] final state particles, a new event-mixing technique is proposed. The new technique introduces a new mixing constraint, namely energy hierarchy correspondence (EHC) cut, which requires that two bosons being swapped should be equal in energy hierarchy in their original events. Numerical tests are performed to check the validity of the new mixing method. Compared to the previous proposed mixing technique (He et al., Chin. Phys. C 42 (2018) 074004), this new method has smaller systematic uncertainties, improving the accuracy of fit BEC parameters.

APA, Harvard, Vancouver, ISO, and other styles

10

Premoselli, Bruno. "A pointwise finite-dimensional reduction method for a fully coupled system of Einstein–Lichnerowicz type." Communications in Contemporary Mathematics 20, no. 06 (August 27, 2018): 1750076. http://dx.doi.org/10.1142/s0219199717500766.

Full text

Abstract:

We construct non-compactness examples for the fully coupled Einstein–Lichnerowicz constraint system in the focusing case. The construction is obtained by combining pointwise a priori asymptotic analysis techniques, finite-dimensional reductions and a fixed-point argument. More precisely, we perform a fixed-point procedure on the remainders of the expected blow-up decomposition. The argument consists of an involved finite-dimensional reduction coupled with a ping-pong method. To overcome the non-variational structure of the system, we work with remainders which belong to strong function spaces and not merely to energy spaces. Performing both the ping-pong argument and the finite-dimensional reduction therefore heavily relies on the a priori pointwise asymptotic techniques of the [Formula: see text] theory.

APA, Harvard, Vancouver, ISO, and other styles

11

Lin, Zhi-Qiang, Bo Tian, Ming Wang, and Xing Lu. "Integrability and Multi-Soliton Solutions for a Variable-Coefficient Coupled Gross–Pitaevskii System for Atomic MatterWaves." Zeitschrift für Naturforschung A 67, no. 10-11 (November 1, 2012): 525–33. http://dx.doi.org/10.5560/zna.2012-0044.

Full text

Abstract:

Under investigation in this paper is a variable-coefficient coupled Gross-Pitaevskii (GP) system, which is associated with the studies on atomic matter waves. Through the Painlev´e analysis, we obtain the constraint on the variable coefficients, under which the system is integrable. The bilinear form and multi-soliton solutions are derived with the Hirota bilinear method and symbolic computation. We found that: (i) in the elastic collisions, an external potential can change the propagation of the soliton, and thus the density of the matter wave in the two-species Bose-Einstein condensate (BEC); (ii) in the shape-changing collision, the solitons can exchange energy among different species, leading to the change of soliton amplitudes.We also present the collisions among three solitons of atomic matter waves.

APA, Harvard, Vancouver, ISO, and other styles

12

SU, GANG, and MASUO SUZUKI. "TOWARDS BOSE–EINSTEIN CONDENSATION OF ELECTRON PAIRS: ROLE OF SCHWINGER BOSONS." International Journal of Modern Physics B 13, no. 08 (March 30, 1999): 925–37. http://dx.doi.org/10.1142/s0217979299000771.

Full text

Abstract:

It can be shown that the bosonic degree of freedom of the tightly bound on-site electron pairs could be separated as Schwinger bosons. This is implemented by projecting the whole Hilbert space into the Hilbert subspace spanned by states of two kinds of Schwinger bosons (to be called binon and vacanon) subject to a constraint that these two kinds of bosonic quasiparticles cannot occupy the same site. We argue that a binon is actually a kind of quantum fluctuations of electron pairs, and a vacanon corresponds to a vacant state. These two bosonic quasiparticles may be responsible for the Bose–Einstein condensation (BEC) of the system associated with electron pairs. These concepts are also applied to the attractive Hubbard model with strong coupling, showing that it is quite useful. The relevance of the present arguments to the existing theories associated with the BEC of electron pairs is briefly commented.

APA, Harvard, Vancouver, ISO, and other styles

13

Dutta, Sourav, Madan Mohan Panja, and Subenoy Chakraborty. "A study of dynamical equations for non-minimally coupled scalar field using Noether symmetric approach." Modern Physics Letters A 31, no. 19 (June 21, 2016): 1650116. http://dx.doi.org/10.1142/s0217732316501169.

Full text

Abstract:

Non-minimally coupled scalar field cosmology has been studied in this work within the framework of Einstein gravity. In the background of homogeneous and isotropic Friedmann–Lemaitre–Robertson–Walker (FLRW) spacetime non-minimally coupled scalar field having self-interacting potential is taken as the source of the matter content. The constraint of imposing Noether symmetry on the Lagrangian of the system not only determines the infinitesimal generator (the symmetry vector) but also the coupling function and the self-interacting potential for the scalar field. By choosing appropriately a point transformation in the augmented space, one of the transformed variables is cyclic for the Lagrangian. Finally, using constants of motion, the solutions are analyzed.

APA, Harvard, Vancouver, ISO, and other styles

14

Araujo, A., and J. G. Pereira. "Entropy in locally-de Sitter spacetimes." International Journal of Modern Physics D 24, no. 14 (December 2015): 1550099. http://dx.doi.org/10.1142/s0218271815500996.

Full text

Abstract:

As quotient spaces, Minkowski and de Sitter are fundamental spacetimes in the sense that they are known a priori, independently of Einstein equation. They represent different nongravitational backgrounds for the construction of physical theories. If general relativity is constructed on a de Sitter spacetime, the underlying kinematics will no longer be ruled by Poincaré, but by the de Sitter group. In this case the definition of diffeomorphism changes, producing concomitant changes in the notions of energy and entropy. These changes are explicitly discussed for the case of the Schwarzschild solution, in which the black hole and the de Sitter horizons show up as a unique entangled system. Such entanglement, together with energy conservation, create a constraint between the black hole activity and the evolution of the de Sitter radius, providing a new scenario for the study of cosmology.

APA, Harvard, Vancouver, ISO, and other styles

15

Sulaiman, Tukur Abdulkadir, Usman Younas, Abdullahi Yusuf, Muhammad Younis, Muhammad Bilal, and Shafqat-Ur-Rehman. "Extraction of new optical solitons and MI analysis to three coupled Gross–Pitaevskii system in the spinor Bose–Einstein condensate." Modern Physics Letters B 35, no. 06 (January 11, 2021): 2150109. http://dx.doi.org/10.1142/s0217984921501098.

Full text

Abstract:

This article investigates the optical solitons to the three coupled Gross–Pitaevskii (GP) system (also called the non-linear Schrödinger (NLS) equation), which describes the [Formula: see text] spinor Bose–Einstein condensate, with [Formula: see text] denoting the atom’s spin. The solutions are expressed in the form of hyperbolic function solutions that have different physical meanings such that the hyperbolic tangent appears in the calculation and rapidity of special relativity while, the hyperbolic cotangent arises in the Langevin function for magnetic polarization, the hyperbolic secant arises in the profile of a laminar jet. The various kinds of soliton solutions in single and combined form like bright, dark, singular as well as bright-dark and singular in the mixed form are also extracted by the mean of extended sinh-Gordon equation expansion method. By using the appropriate values of the involved parameters, 3D, 2D and their corresponding contour graphs are sketched for physical movement of the attained results. We also discuss the modulation instability (MI) analysis of the governing model. The constraint conditions for the existence of soliton solutions are also mentioned. The calculated work and earned results show the power, effectiveness, and the simplicity of applied method to discuss the soliton solutions as the contrast with other analytical schemes. The main outcome of the proposed technique is that we have succeeded in a single move to get and organize various types of new solutions.

APA, Harvard, Vancouver, ISO, and other styles

16

Wertz, O., D. Stern, A. Krone-Martins, L. Delchambre, C. Ducourant, U. Gråe Jørgensen, M. Dominik, et al. "Gaia GraL: Gaia DR2 gravitational lens systems." Astronomy & Astrophysics 628 (July 29, 2019): A17. http://dx.doi.org/10.1051/0004-6361/201834573.

Full text

Abstract:

We report the spectroscopic confirmation and modeling of the quadruply imaged quasar GRAL 113100–441959, the first gravitational lens (GL) to be discovered from a machine learning technique that only relies on the relative positions and fluxes of the observed images without considering colour informations. Follow-up spectra obtained with Keck/LRIS reveal the lensing nature of this quadruply imaged quasar with redshift zs = 1.090 ± 0.002, but show no evidence of the central lens galaxy. Using the image positions and G-band flux ratios provided by Gaia Data Release 2 as constraints, we modeled the system with a singular power-law elliptical mass distribution (SPEMD) plus external shear, to different levels of complexity. We show that relaxing the isothermal constraint of the SPEMD does not lead to statistically significant different results in terms of fitting the lensing data. We thus simplified the SPEMD to a singular isothermal ellipsoid to estimate the Einstein radius of the main lens galaxy θE = 0.″851, the intensity and position angle of the external shear (γ,θγ) = (0.044, 11.°5), and we predict the lensing galaxy position to be (θgal,1, θgal,2) = (−0.″424, −0.″744) with respect to image A. We provide time delay predictions for pairs of images, assuming a plausible range of lens redshift values zl between 0.5 and 0.9. Finally, we examine the impact on time delays of the so-called source position transformation, a family of degeneracies existing between different mass density profiles that reproduce most of the lensing observables equally well. We show that this effect contributes significantly to the time delay error budget and cannot be ignored during the modeling. This has implications for robust cosmography applications of lensed systems. GRAL 113100–441959 is the first in a series of seven new spectroscopically confirmed GLs discovered from Gaia Data Release 2.

APA, Harvard, Vancouver, ISO, and other styles

17

O’Riordan, C. M., S. J. Warren, and D. J. Mortlock. "Galaxy mass profiles from strong lensing I: the circular power-law model." Monthly Notices of the Royal Astronomical Society 487, no. 4 (June 20, 2019): 5143–54. http://dx.doi.org/10.1093/mnras/stz1603.

Full text

Abstract:

Abstract In this series of papers, we develop a formalism for constraining mass profiles in strong gravitational lenses with extended images, using fluxes in addition to positional information. We start in this paper with a circular power-law profile and show that the slope γ is uniquely determined by only two observables: the flux ratio f1/f2 and the image position ratio θ1/θ2 of the two images. We derive an analytic expression relating these two observables to the slope, a result that does not depend on the Einstein angle or the structure or brightness of the source. We then find an expression for the uncertainty on the slope σγ that depends only on the position ratio θ1/θ2 and the total signal-to-noise ratio (S/N) in the images. For example, in a system with position ratio θ1/θ2 = 0.5, S/N = 100, and γ = 2 we find that γ is constrained to a precision of ±0.03. We then test these results against a series of mock observations. We invert the images and fit an 11-parameter model, including ellipticity and position angle for both lens and source and measure the uncertainty on γ. We find agreement with the theoretical estimate for all mock observations. In future papers, we will examine the radial range of the galaxy over which the constraint on the slope applies, and extend the analysis to elliptical lenses.

APA, Harvard, Vancouver, ISO, and other styles

18

Aziz, Abdul, Saibal Ray, Farook Rahaman, M. Khlopov, and B. K. Guha. "Constraining values of bag constant for strange star candidates." International Journal of Modern Physics D 28, no. 13 (October 2019): 1941006. http://dx.doi.org/10.1142/s0218271819410062.

Full text

Abstract:

We provide a strange star model under the framework of general relativity by using a general linear equation of state (EOS). The solution set thus obtained is employed on altogether 20 compact star candidates to constraint values of MIT bag model. No specific value of the bag constant ([Formula: see text]) a priori is assumed, rather possible range of values for bag constant is determined from observational data of the said set of compact stars. To do so, the Tolman–Oppenheimer–Volkoff (TOV) equation is solved by homotopy perturbation method (HPM) and hence we get a mass function for the stellar system. The solution to the Einstein field equations represents a nonsingular, causal and stable stellar structure which can be related to strange stars. Eventually, we get an interesting result on the range of the bag constant as [Formula: see text]. We have found the maximum surface redshift [Formula: see text] and shown that the central redshift ([Formula: see text]) cannot have value larger than [Formula: see text], where [Formula: see text]. Also, we provide a possible value of bag constant for neutron star with quark core using hadronic as well as quark EOS.

APA, Harvard, Vancouver, ISO, and other styles

19

Zakharov, Alexander F. "Tests of gravity theories with Galactic Center observations." International Journal of Modern Physics D 28, no. 13 (October 2019): 1941003. http://dx.doi.org/10.1142/s0218271819410037.

Full text

Abstract:

An active stage of relativistic astrophysics started in 1963 since in this year, quasars were discovered, Kerr solution had been found and the first Texas Symposium on Relativistic Astrophysics was organized in Dallas. Five years later, in 1967–1968 pulsars were discovered and their model as rotating neutron stars (NSs) had been proposed, meanwhile Wheeler claimed that Kerr and Schwarzschild vacuum solutions of Einstein equations provide an efficient approach for astronomical objects with different masses. Wheeler suggested to call these objects black holes. NSs were observed in different spectral band of electromagnetic radiation. In addition, a neutrino signal had been found for SN1987A. Therefore, multi-messenger astronomy demonstrated its efficiency for decades even before observations of the first gravitational radiation sources. However, usually, one has only manifestations of black holes in a weak gravitational field limit and sometimes a model with a black hole could be substituted with an alternative approach which very often looks much less natural, however, it is necessary to find observational evidences to reject such an alternative model. At the moment, only few astronomical signatures for strong gravitational field are found, including a shape of relativistic iron [Formula: see text] line, size and shape of shadows near black holes at the Galactic Center (GC) and M87, trajectories of bright stars near the GC. After two observational runs, the LIGO–Virgo collaboration provided a confirmation for a presence of mergers for 10 binary black holes and one binary NS system where gravitational wave signals were found. In addition, in the last years, a remarkable progress has been reached in a development of observational facilities to investigate a gravitational potential, for instance, the number of telescopes operating in the Event Horizon Telescope network is increasing and accuracy of a shadow reconstruction near the GC is improving, meanwhile largest VLT, Keck telescopes with adaptive optics and especially GRAVITY facilities observe bright IR stars at the GC with perfect accuracy. More options for precision observations of bright stars will be available with creating extremely large telescopes Thirty Meter Telescope (TMT) and E-ELT. It is clear that the GC (Sgr [Formula: see text]) is a specific object for observations. Our solar system is located at a distance around 8 kpc from the GC. Earlier, theorists proposed a number of different models including exotic ones for GC such as boson star, fermion ball, neutrino ball, a cluster of NSs. Later, some of these models were ruled out or essentially constrained with consequent observations and theoretical considerations. Currently, a supermassive black hole with mass around [Formula: see text] is the most natural model for GC. Using results of observations for trajectories of bright stars in paper [A. F. Zakharov, P. Jovanović, D. Borka and V. B. Jovanović, J. Cosmol. Astropart. Phys. 05 (2016) 045] the authors got a graviton mass constraint which is comparable and consistent with constraints obtained recently by the LIGO–Virgo collaboration. Later, we consider opportunities to improve current graviton mass constraints with future observations of bright stars [A. F. Zakharov, P. Jovanović, D. Borka and V. B. Jovanović, J. Cosmol. Astropart. Phys. 04 (2018) 050]. Similarly, from an analysis of bright star trajectories, one could constrain a tidal charge which was predicted by a gravity theory with an additional dimension [A. F. Zakharov, Eur. Phys. J. C 78 (2018) 689].

APA, Harvard, Vancouver, ISO, and other styles

20

Amante, Mario H., Juan Magaña, V. Motta, Miguel A. García-Aspeitia, and Tomás Verdugo. "Testing dark energy models with a new sample of strong-lensing systems." Monthly Notices of the Royal Astronomical Society 498, no. 4 (September 12, 2020): 6013–33. http://dx.doi.org/10.1093/mnras/staa2760.

Full text

Abstract:

ABSTRACT Inspired by a new compilation of strong-lensing systems, which consist of 204 points in the redshift range 0.0625 < zl < 0.958 for the lens and 0.196 < zs < 3.595 for the source, we constrain three models that generate a late cosmic acceleration: the ω-cold dark matter model, the Chevallier–Polarski–Linder, and the Jassal–Bagla–Padmanabhan parametrizations. Our compilation contains only those systems with early-type galaxies acting as lenses, with spectroscopically measured stellar velocity dispersions, estimated Einstein radius, and both the lens and source redshifts. We assume an axially symmetric mass distribution in the lens equation, using a correction to alleviate differences between the measured velocity dispersion (σ) and the dark matter halo velocity dispersion (σDM) as well as other systematic errors that may affect the measurements. We have considered different subsamples to constrain the cosmological parameters of each model. Additionally, we generate a mock data of SLS to asses the impact of the chosen mass profile on the accuracy of Einstein radius estimation. Our results show that cosmological constraints are very sensitive to the selected data: Some cases show convergence problems in the estimation of cosmological parameters (e.g. systems with observed distance ratio Dobs < 0.5), others show high values for the χ2 function (e.g. systems with a lens equation Dobs > 1 or high velocity dispersion σ > 276 km s−1). However, we obtained a fiduciary sample with 143 systems, which improves the constraints on each tested cosmological model.

APA, Harvard, Vancouver, ISO, and other styles

21

Manna, Tuhina, Bidisha Samanta, Amna Ali, and Farook Rahaman. "Solar system tests in Einstein–æther gravity." Canadian Journal of Physics 99, no. 8 (August 2021): 681–90. http://dx.doi.org/10.1139/cjp-2021-0020.

Full text

Abstract:

In the current paper we analyse the three classical tests of general relativity, namely, the precession of perihelion, deflection of light, and time delay in Einstein–æther gravity. Einstein–æther gravity has two static, spherically symmetric, charged black hole solutions corresponding to different constraints on its coupling constants c14 and c123. We investigate the aforementioned tests for both these solutions, graphically and analytically. We also tabulate our results and discuss the outcome, which is promising. We evaluate the results, when the coupling constants are varied over a vast range of values, both within the constraints set by the recent observational data, and also beyond, for a comparative study.

APA, Harvard, Vancouver, ISO, and other styles

22

NIETO, J. A., E. A. LEÓN, and V. M. VILLANUEVA. "HIGHER-DIMENSIONAL CHARGED BLACK HOLES AS CONSTRAINED SYSTEMS." International Journal of Modern Physics D 22, no. 07 (June 2013): 1350047. http://dx.doi.org/10.1142/s0218271813500478.

Full text

Abstract:

We construct a Lagrangian and Hamiltonian formulation for charged black holes in a d-dimensional maximally symmetric spherical space. By considering first new variables that give raise to an interesting dimensional reduction of the problem, we show that the introduction of a charge term is compatible with classical solutions to Einstein equations. In fact, we derive the well-known solutions for charged black holes, specially in the case of d = 4, where the Reissner–Nordström solution holds, without reference to Einstein field equations. We argue that our procedure may be of help for clarifying symmetries, dynamics and some quantum aspects of black holes.

APA, Harvard, Vancouver, ISO, and other styles

23

GENTLE, ADRIAN P. "THE BSSN FORMULATION IS A PARTIALLY CONSTRAINED EVOLUTION SYSTEM." International Journal of Modern Physics D 19, no. 02 (February 2010): 153–58. http://dx.doi.org/10.1142/s0218271810016312.

Full text

Abstract:

It is shown that the BSSN formulation of the Einstein equations, which forms the basis of most simulations in numerical relativity, explicitly uses the momentum constraints to evolve the conformal connection coefficients.

APA, Harvard, Vancouver, ISO, and other styles

24

CARDONE, F., R. MIGNANI, W. PERCONTI, A. PETRUCCI, and R. SCRIMAGLIO. "THE SHADOW OF LIGHT: LORENTZ INVARIANCE AND COMPLEMENTARITY PRINCIPLE IN ANOMALOUS PHOTON BEHAVIOR." International Journal of Modern Physics B 20, no. 09 (April 10, 2006): 1107–21. http://dx.doi.org/10.1142/s0217979206033735.

Full text

Abstract:

We review the results of two double-slit-like experiments in the infrared range, which evidence an anomalous behavior of photon systems under particular (energy and space) constraints. These outcomes (independently confirmed by crossing photon beam experiments in both the optical and the microwave range) apparently rule out the Copenhagen interpretation of the quantum wave, i.e. the probability wave, by admitting an interpretation in terms of the Einstein–de Broglie–Bohm hollow wave for photons. Moreover, these experiments support the interpretation of the hollow wave as a deformation of the Minkowski space-time geometry. We stress the implications of these experimental results and of their interpretation for the concept of action-at-a-distance, Einstein's relativistic correlation and Bohr's principle of complementarity,

APA, Harvard, Vancouver, ISO, and other styles

25

KIRIUSHCHEVA, N., and S. V. KUZMIN. "ON THE HAMILTONIAN FORMULATION OF THE EINSTEIN–HILBERT ACTION IN TWO DIMENSIONS." Modern Physics Letters A 21, no. 11 (April 10, 2006): 899–905. http://dx.doi.org/10.1142/s0217732306020202.

Full text

Abstract:

It is shown that if general covariance is to be preserved (i.e. a coordinate system is not fixed) the well-known triviality of the Einstein field equations in two dimensions is not a sufficient condition for the Einstein–Hilbert action to be a total divergence. Consequently, a Hamiltonian formulation is possible without any modification of the two-dimensional Einstein–Hilbert action. We find the resulting constraints and the corresponding gauge transformations of the metric tensor.

APA, Harvard, Vancouver, ISO, and other styles

26

Tadmon, Calvin. "On the constraints problem for the Einstein–Yang–Mills–Higgs system." Journal of Fixed Point Theory and Applications 14, no. 2 (December 2013): 419–56. http://dx.doi.org/10.1007/s11784-014-0164-5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

27

Jozefiak, Adam, and Jim Zhang Hao Li. "Modelling Diffusion in a Physically Constrained System: A Numerical Approach." STEM Fellowship Journal 2, no. 1 (July 1, 2016): 38–48. http://dx.doi.org/10.17975/sfj-2016-008.

Full text

Abstract:

Diffusion has been described on a microscopic scale by Einstein as a probabilistic collision of particles. On a macroscale, diffusion has been thoroughly described by Fick’s laws. However, the solutions to Fick’s laws are limited to idealized physical systems. The aim of this experimental study is to provide a mathematical model for diffusion which incorporates both macroscopic and microscopic properties to effectively model diffusion in a geometrically constrained two-dimensional system. Based on macroscopic and microscopic properties, two-dimensional diffusion was modelled as a summation of equally probable paths of diffusion. The point source diffusion of hydrochloric acid in an arena with variable barrier dimensions was monitored continuously using a pH probe. The numerical solution of the mathematical model for each experimental condition was determined and the pre-exponential factor was fit to the measurements. The average pre-exponential value was determined for each experimental condition, and t-scores were calculated to compare the average pre-exponential values which were found to be statistically similar. This indicates that the proposed model is an accurate model as it predicts identical pre-exponential values between experimental conditions, accounting for all variants that it attempts to model. This model provides a bridge between the microscopic and macrcoscopic theoretical descriptions of diffusion that were independently postulated by Einstein and Fick. Applications of the model include the approximation of locations of leakage in hydraulic systems.

APA, Harvard, Vancouver, ISO, and other styles

28

Warren, S. J., P. C. Hewett, G. F. Lewis, P. Møller, A. Iovino, and P. A. Shaver. "Identifying Optical Einstein Rings." Symposium - International Astronomical Union 173 (1996): 329–34. http://dx.doi.org/10.1017/s0074180900231690.

Full text

Abstract:

The discovery of gravitationally lensed radio-rings (Hewitt et al. 1988) opened up a new line of attack on the problem of dark matter in galaxies. High–resolution radio observations (Langston et al. 1989) resolve structure tangentially and radially within the rings, providing sophisticated analysis routines (Kochanek & Narayan 1992, Wallington, Narayan & Kochanek 1994) with enough constraints to compute realistic models of the mass distribution within the deflectors (Kochanek 1995). Five such systems are now known and extensive programs to identify further examples are underway.

APA, Harvard, Vancouver, ISO, and other styles

29

Bruneton, J. P., M. Rinaldi, A. Kanfon, A. Hees, S. Schlögel, and A. Füzfa. "Fab Four: When John and George Play Gravitation and Cosmology." Advances in Astronomy 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/430694.

Full text

Abstract:

Scalar-tensor theories of gravitation attract again a great interest since the discovery of the Chameleon mechanism and of the Galileon models. The former allows reconciling the presence of a scalar field with the constraints from Solar System experiments. The latter leads to inflationary models that do not need ad hoc potentials. Further generalizations lead to a tensor-scalar theory, dubbed the “Fab Four,” with only first and second order derivatives of the fields in the equations of motion that self-tune to a vanishing cosmological constant. This model needs to be confronted with experimental data in order to constrain its large parameter space. We present some results regarding a subset of this theory named “John,” which corresponds to a nonminimal derivative coupling between the scalar field and the Einstein tensor in the action. We show that this coupling gives rise to an inflationary model with very unnatural initial conditions. Thus, we include the term named “George,” namely, a nonminimal, but nonderivative, coupling between the scalar field and Ricci scalar. We find a more natural inflationary model, and, by performing a post-Newtonian analysis, we derive the set of equations that constrain the parameter space with data from experiments in the Solar System.

APA, Harvard, Vancouver, ISO, and other styles

30

Collett, Thomas E., Lindsay J. Oldham, Russell J. Smith, Matthew W. Auger, Kyle B. Westfall, David Bacon, Robert C. Nichol, Karen L. Masters, Kazuya Koyama, and Remco van den Bosch. "A precise extragalactic test of General Relativity." Science 360, no. 6395 (June 21, 2018): 1342–46. http://dx.doi.org/10.1126/science.aao2469.

Full text

Abstract:

Einstein’s theory of gravity, General Relativity, has been precisely tested on Solar System scales, but the long-range nature of gravity is still poorly constrained. The nearby strong gravitational lens ESO 325-G004 provides a laboratory to probe the weak-field regime of gravity and measure the spatial curvature generated per unit mass, γ. By reconstructing the observed light profile of the lensed arcs and the observed spatially resolved stellar kinematics with a single self-consistent model, we conclude that γ = 0.97 ± 0.09 at 68% confidence. Our result is consistent with the prediction of 1 from General Relativity and provides a strong extragalactic constraint on the weak-field metric of gravity.

APA, Harvard, Vancouver, ISO, and other styles

31

Nair, S. "A Lens Model For B0218+357." Symposium - International Astronomical Union 173 (1996): 197–98. http://dx.doi.org/10.1017/s007418090023129x.

Full text

Abstract:

The smallest radio Einstein Ring, B2018+357, discovered by Patnaik et al. (1993), shows much promise as a tool to constrain the parameters of cosmological models (Refsdal 1964). Dominating this system is a pair of 0.″335–separation compact radio images, with image A between 2.7 to 3.9 times as strong as image B (λλ 18 to 2 cm). Observations have established the lens redshift (zl = 0.685, O'Dea et al. 1992, Browne et al. 1993), a possible source redshift (zs = 0.96, Lawrence, this conference), and a tentative value for the time–delay between the highly polarized images A and B (12 ± 3 days, Browne, this conference). Recent mas–resolution observations have made it possible to understand the imaging of A and B in sufficient detail as to provide constraints on an elliptical lens model for B0218+357; this work presents a model and provides an estimate of Hubble's Constant.

APA, Harvard, Vancouver, ISO, and other styles

32

March, Riccardo, Giovanni Bellettini, Roberto Tauraso, and Simone Dell’Agnello. "CONSTRAINING SPACETIME TORSION WITH THE MOON, MERCURY AND LAGEOS." Acta Polytechnica 53, A (December 18, 2013): 817–20. http://dx.doi.org/10.14311/ap.2013.53.0817.

Full text

Abstract:

We consider an extension of Einstein General Relativity where, beside the Riemann curvature tensor, we suppose the presence of a torsion tensor. Using a parametrized theory based on symmetry arguments, we report on some results concerning the constraints that can be put on torsion parameters by studying the orbits of a test body in the solar system.

APA, Harvard, Vancouver, ISO, and other styles

33

Gutiérrez-Piñeres, Antonio C., Cesar S. López-Monsalvo, and Francisco Nettel. "Two-Dimensional Einstein Manifolds in Geometrothermodynamics." Advances in High Energy Physics 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/967618.

Full text

Abstract:

We present a class of thermodynamic systems with constant thermodynamic curvature which, within the context of geometric approaches of thermodynamics, can be interpreted as constant thermodynamic interaction among their components. In particular, for systems constrained by the vanishing of the Hessian curvature we write down the systems of partial differential equations. In such a case it is possible to find a subset of solutions lying on a circumference in an abstract space constructed from the first derivatives of the isothermal coordinates. We conjecture that solutions on the characteristic circumference are of physical relevance, separating them from those of pure mathematical interest. We present the case of a one-parameter family of fundamental relations that—when lying in the circumference—describe a polytropic fluid.

APA, Harvard, Vancouver, ISO, and other styles

34

PADMANABHAN, T. "PROBING THE QUANTUM MICROSTRUCTURE OF SPACE–TIME." Modern Physics Letters A 14, no. 24 (August 10, 1999): 1667–72. http://dx.doi.org/10.1142/s0217732399001759.

Full text

Abstract:

The question of how tightly one can constrain the microscopic theory of quantum gravity from the known features of low energy gravity is addressed. To begin with, from the very fact that our universe made a transition from a quantum regime to classical one, it is possible to conclude that infinite number of degrees of freedom had to be integrated out from the fundamental theory to obtain the low energy Einstein Lagrangian. Further constraints can be imposed from the fact that the quantum state describing a black hole has to possess certain universal form of density of states, in any microscopic description of space–time, which can be ascertained from general considerations. Since a black hole can be formed from the collapse of any physical system with a low energy (E ≪ Ep) Hamiltonian H, it is possible to obtain the form the effective high energy (E ≫ Ep) Hamiltonian from general consideration. These results provide the physical reasons for some of the mathematical features underlying string theories and other models for quantum gravity.

APA, Harvard, Vancouver, ISO, and other styles

35

Yoneda, Gen, and Hisa-aki Shinkai. "Hyperbolic formulations and numerical relativity: II. asymptotically constrained systems of Einstein equations." Classical and Quantum Gravity 18, no. 3 (January 18, 2001): 441–62. http://dx.doi.org/10.1088/0264-9381/18/3/307.

Full text

APA, Harvard, Vancouver, ISO, and other styles

36

VACARU, S. "ON GENERAL SOLUTIONS OF EINSTEIN EQUATIONS." International Journal of Geometric Methods in Modern Physics 08, no. 01 (February 2011): 9–21. http://dx.doi.org/10.1142/s0219887811004938.

Full text

Abstract:

We show how the Einstein equations with cosmological constant (and/or various types of matter field sources) can be integrated in a very general form following the anholonomic deformation method for constructing exact solutions in four- and five-dimensional gravity (S. Vacaru, IJGMMP 4 (2007) 1285). In this paper, we prove that such a geometric method can be used for constructing general non-Killing solutions. The key idea is to introduce an auxiliary linear connection which is also metric compatible and completely defined by the metric structure but contains some torsion terms induced nonholonomically by generic off-diagonal coefficients of metric. There are some classes of nonholonomic frames with respect to which the Einstein equations (for such an auxiliary connection) split into an integrable system of partial differential equations. We have to impose additional constraints on generating and integration functions in order to transform the auxiliary connection into the Levi-Civita one. This way, we extract general exact solutions (parametrized by generic off-diagonal metrics and depending on all coordinates) in Einstein gravity and five-dimensional extensions.

APA, Harvard, Vancouver, ISO, and other styles

37

Collett, Thomas E., and Russell J. Smith. "A triple rollover: a third multiply imaged source at z ≈ 6 behind the Jackpot gravitational lens." Monthly Notices of the Royal Astronomical Society 497, no. 2 (June 23, 2020): 1654–60. http://dx.doi.org/10.1093/mnras/staa1804.

Full text

Abstract:

ABSTRACT Using a 5-h adaptive-optics-assisted observation with Multi-Unit Spectroscopic Explorer, we have identified a doubly imaged Ly α source at a redshift of 5.975 behind the z = 0.222 lens galaxy J0946+1006 (the ‘Jackpot’). The source separation implies an Einstein radius of ∼2.5 arcsec. Combined with the two previously known Einstein rings in this lens (radii 1.4 arcsec at z = 0.609 and 2.1 arcsec at z ≈ 2.4), this system is now a unique galaxy-scale triple-source-plane lens. We show that existing lensing models for J0946+1006 successfully map the two new observed images to a common point on the z = 5.975 source plane. The new source will provide further constraints on the mass distribution in the lens and in the two previously known sources. The third source also probes two new distance scaling factors that are sensitive to the cosmological parameters of the Universe. We show that detection of a new multiply imaged emission-line source is not unexpected in observations of this depth; similar data for other known lenses should reveal a larger sample of multiple-image-plane systems for cosmography and other applications.

APA, Harvard, Vancouver, ISO, and other styles

38

Noundjeu, P., N. Noutchegueme, and A. D. Rendall. "Existence of initial data satisfying the constraints for the spherically symmetric Einstein–Vlasov–Maxwell system." Journal of Mathematical Physics 45, no. 2 (February 2004): 668–76. http://dx.doi.org/10.1063/1.1637713.

Full text

APA, Harvard, Vancouver, ISO, and other styles

39

He, Q., T. Li, X. He, and K. Zhuang. "Sub-regional event mixing constraints for two-pion Bose–Einstein correlations measurements in ππx system." International Journal of Modern Physics E 28, no. 04 (April 2019): 1950024. http://dx.doi.org/10.1142/s0218301319500241.

Full text

Abstract:

Current BEC measurements in exclusive reactions with very low multiplicities is still a big challenge due to lack of effective observing method. Previously proposed observing approaches using event mixing technique still face problems of sample reduction and introducing extra and unnecessary fitting parameters. Here, we show the viability of a new event mixing approach with sub-regional mixing constraints related to energy hierarchy and energy sum observables. Extensive numerical simulations are performed to test the new mixing technique. Its ability to observe BEC parameters is validated and the systematic bias of the fit BEC parameter [Formula: see text] is improved since this new approach reduces the fitting parameters from 4 to 3 compared to the previously proposed mixing method.

APA, Harvard, Vancouver, ISO, and other styles

40

VASILIEV, M. A. "ACTIONS, CHARGES AND OFF-SHELL FIELDS IN THE UNFOLDED DYNAMICS APPROACH." International Journal of Geometric Methods in Modern Physics 03, no. 01 (February 2006): 37–80. http://dx.doi.org/10.1142/s0219887806001016.

Full text

Abstract:

Within unfolded dynamics approach, we represent actions and conserved charges as elements of cohomology of the L∞ algebra underlying the unfolded formulation of a given dynamical system. The unfolded off-shell constraints for symmetric fields of all spins in Minkowski space are shown to have the form of zero curvature and covariant constancy conditions for 1-forms and 0-forms taking values in an appropriate star product algebra. Unfolded formulation of Yang–Mills and Einstein equations is presented in a closed form.

APA, Harvard, Vancouver, ISO, and other styles

41

Cao, Zhoujian, Pei Fu, Li-Wei Ji, and Yinhua Xia. "Application of local discontinuous Galerkin method to Einstein equations." International Journal of Modern Physics D 28, no. 01 (January 2019): 1950014. http://dx.doi.org/10.1142/s0218271819500147.

Full text

Abstract:

Finite difference and pseudo-spectral methods have been widely used in the numerical relativity to solve the Einstein equations. As the third major category method to solve partial differential equations, finite element method is less frequently used in numerical relativity. In this paper, we design a finite element algorithm to solve the evolution part of the Einstein equations. This paper is the second one of a systematic investigation of applying adaptive finite element method to the Einstein equations, especially aiming for binary compact objects simulations. The first paper of this series has been contributed to the constrained part of the Einstein equations for initial data. Since applying finite element method to the Einstein equations is a big project, we mainly propose the theoretical framework of a finite element algorithm together with local discontinuous Galerkin method for the Einstein equations in the current work. In addition, we have tested our algorithm based on the spherical symmetric spacetime evolution. In order to simplify our numerical tests, we have reduced the problem to a one-dimensional space problem by taking the advantage of the spherical symmetry. Our reduced equation system is a new formalism for spherical symmetric spacetime simulation. Based on our test results, we find that our finite element method can capture the shock formation which is introduced by numerical error. In contrast, such shock is smoothed out by numerical dissipation within the finite difference method. We suspect this is partly the reason that the accuracy of finite element method is higher than the finite difference method. At the same time, different kinds of formulation parameters setting are also discussed.

APA, Harvard, Vancouver, ISO, and other styles

42

Ray, Amritansu, and S. K. Majumder. "Derivation of some new distributions in statistical mechanics using maximum entropy approach." Yugoslav Journal of Operations Research 24, no. 1 (2014): 145–55. http://dx.doi.org/10.2298/yjor120912031r.

Full text

Abstract:

The maximum entropy principle has been earlier used to derive the Bose Einstein(B.E.), Fermi Dirac(F.D.) & Intermediate Statistics(I.S.) distribution of statistical mechanics. The central idea of these distributions is to predict the distribution of the microstates, which are the particle of the system, on the basis of the knowledge of some macroscopic data. The latter information is specified in the form of some simple moment constraints. One distribution differs from the other in the way in which the constraints are specified. In the present paper, we have derived some new distributions similar to B.E., F.D. distributions of statistical mechanics by using maximum entropy principle. Some proofs of B.E. & F.D. distributions are shown, and at the end some new results are discussed.

APA, Harvard, Vancouver, ISO, and other styles

43

Patenou, Jean Baptiste. "Cauchy problem on a characteristic cone for the Einstein–Vlasov system: (I) The initial data constraints." Comptes Rendus Mathematique 355, no. 2 (February 2017): 187–92. http://dx.doi.org/10.1016/j.crma.2016.11.018.

Full text

APA, Harvard, Vancouver, ISO, and other styles

44

KAMIMURA, KIYOSHI, SHINOBU MAKITA, and TAKESHI FUKUYAMA. "METRIC FROM NONMETRIC ACTION OF GRAVITY." International Journal of Modern Physics D 01, no. 02 (January 1992): 363–70. http://dx.doi.org/10.1142/s0218271892000185.

Full text

Abstract:

The action of general relativity proposed by Capovilla, Jacobson and Dell is written in terms of SO(3) gauge fields and gives Ashtekar's constraints for Einstein gravity. However, it does not depend on the spacetime metric nor its signature explicitly. We discuss how the spacetime metric is introduced from algebraic relations of the constraints and the form of the Hamiltonian by focusing our attention on the signature factor. The system describes both Euclidean and Lorentzian metrics depending on reality assignments of the gauge connections. That is, Euclidean metrics arise from the real gauge fields. On the other hand, self-duality of the gauge fields, which is well known in the Ashtekar formalism, is derived in this theory from the consistency condition of the Lorentzian metric. We also show that the metric so determined is equivalent to that given by Urbantke, which is usually accepted as a definition of the metric for this system.

APA, Harvard, Vancouver, ISO, and other styles

45

Gobbo, Gianpaolo, Giovanni Ciccotti, and Bernhardt L. Trout. "On computing the solubility of molecular systems subject to constraints using the extended Einstein crystal method." Journal of Chemical Physics 150, no. 20 (May 28, 2019): 201104. http://dx.doi.org/10.1063/1.5099378.

Full text

APA, Harvard, Vancouver, ISO, and other styles

46

CARDONE, F., R. MIGNANI, W. PERCONTI, A. PETRUCCI, and R. SCRIMAGLIO. "THE SHADOW OF LIGHT: FURTHER EXPERIMENTAL EVIDENCES." International Journal of Modern Physics B 20, no. 01 (January 10, 2006): 85–97. http://dx.doi.org/10.1142/s0217979206033085.

Full text

Abstract:

We report the results of a double-slit-like experiment in the infrared range, which confirm those of a previous one by evidencing an anomalous behaviour of photon systems under particular (energy and space) constraints. These outcomes (independently confirmed by crossing photon beam experiments in both the optical and the microwave range) apparently rule out the Copenhagen interpretation of the quantum wave, i.e. the probability wave, by admitting an interpretation in terms of the Einstein–de Broglie–Bohm hollow wave for photons. Moreover, this second experiment further supports the interpretation of the hollow wave as a deformation of the Minkowski space-time geometry.

APA, Harvard, Vancouver, ISO, and other styles

47

Oost, Jacob, Shinji Mukohyama, and Anzhong Wang. "Spherically Symmetric Exact Vacuum Solutions in Einstein-Aether Theory." Universe 7, no. 8 (July 28, 2021): 272. http://dx.doi.org/10.3390/universe7080272.

Full text

Abstract:

We study spherically symmetric spacetimes in Einstein-aether theory in three different coordinate systems, the isotropic, Painlevè-Gullstrand, and Schwarzschild coordinates, in which the aether is always comoving, and present both time-dependent and time-independent exact vacuum solutions. In particular, in the isotropic coordinates we find a class of exact static solutions characterized by a single parameter c14 in closed forms, which satisfies all the current observational constraints of the theory, and reduces to the Schwarzschild vacuum black hole solution in the decoupling limit (c14=0). However, as long as c14≠0, a marginally trapped throat with a finite non-zero radius always exists, and on one side of it the spacetime is asymptotically flat, while on the other side the spacetime becomes singular within a finite proper distance from the throat, although the geometric area is infinitely large at the singularity. Moreover, the singularity is a strong and spacetime curvature singularity, at which both of the Ricci and Kretschmann scalars become infinitely large.

APA, Harvard, Vancouver, ISO, and other styles

48

Wang, Y. S., B. W. Jeng, and C. S. Chien. "A Two-Parameter Continuation Method for Rotating Two-Component Bose-Einstein Condensates in Optical Lattices." Communications in Computational Physics 13, no. 2 (February 2013): 442–60. http://dx.doi.org/10.4208/cicp.110711.170212a.

Full text

Abstract:

AbstractWe study efficient spectral-collocation and continuation methods (SCCM) for rotating two-component Bose-Einstein condensates (BECs) and rotating two-component BECs in optical lattices, where the second kind Chebyshev polynomials are used as the basis functions for the trial function space. A novel two-parameter continuation algorithm is proposed for computing the ground state and first excited state solutions of the governing Gross-Pitaevskii equations (GPEs), where the classical tangent vector is split into two constraint conditions for the bordered linear systems. Numerical results on rotating two-component BECs and rotating two-component BECs in optical lattices are reported. The results on the former are consistent with the published numerical results.

APA, Harvard, Vancouver, ISO, and other styles

49

Ferdman, Robert D. "PSR J1913+1102: a pulsar in a highly asymmetric and relativistic double neutron star system." Proceedings of the International Astronomical Union 13, S337 (September 2017): 146–49. http://dx.doi.org/10.1017/s1743921317009139.

Full text

Abstract:

AbstractPSR J1913+1102 is a double neutron star system (DNS) discovered in the Pulsar Arecibo L-band Feed Array survey. We have now very precisely measured the rate of advance of periastron for the system and the Einstein delay. From general relativity, this results in precise mass measurements: 1.65 ± 0.05 and 1.24 ± 0.05 M⊙ for the pulsar and neutron-star companion, respectively. This makes PSR J1913+1102 both the most massive double neutron star system known, and the most asymmetric in mass among compact DNS binaries. This asymmetry will allow for stringent limits on the effects of dipolar gravitational-wave radiation, predicted by alternative theories of gravity, as well as insight into heavy-element production from the eventual merger of this system and others like it. Further observations will also tighten constraints on formation and evolution models; this is crucial for understanding the DNS population, for which there are relatively few mass measurements.

APA, Harvard, Vancouver, ISO, and other styles

50

VALTANCOLI, P. "PERTURBATIVE ANALYSIS OF THE TWO-BODY PROBLEM IN (2 + 1)-AdS GRAVITY." International Journal of Modern Physics A 16, no. 17 (July 10, 2001): 2945–63. http://dx.doi.org/10.1142/s0217751x01004232.

Full text

Abstract:

We derive a perturbative scheme to treat the interaction between point sources and AdS-gravity. The interacting problem is equivalent to the search of a polydromic mapping XA = XA (xμ), endowed with O(2,2) monodromies, between the physical coordinate system and a Minkowskian four-dimensional coordinate system, which is however constrained to live on a hypersurface. The physical motion of point sources is therefore mapped to a geodesic motion on this hypersurface. We impose an instantaneous gauge which induces a set of equations defining such a polydromic mapping. Their consistency leads naturally to the Einstein equations in the same gauge. We explore the restriction of the monodromy group to O(2,1), and we obtain the solution of the fields perturbatively in the cosmological constant.

APA, Harvard, Vancouver, ISO, and other styles

Journal articles on the topic 'Einstein constraint system'

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles