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Journal articles on the topic 'Vaidya’s black hole'

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Published: 31 August 2024

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1

IBOHAL, NG, and L. KAPIL. "CHARGED BLACK HOLES IN VAIDYA BACKGROUNDS: HAWKING'S RADIATION." International Journal of Modern Physics D 19, no. 04 (April 2010): 437–64. http://dx.doi.org/10.1142/s0218271810016518.

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In this paper we propose a class of embedded solutions of Einstein's field equations describing nonrotating Reissner–Nordstrom–Vaidya and rotating Kerr–Newman–Vaidya black holes. The Reissner–Nordstrom–Vaidya is obtained by embedding Reissner–Nordstrom solution into the nonrotating Vaidya. Similarly, we also find the Kerr–Newman–Vaidya black hole, when Kerr–Newman embeds into the rotating Vaidya solution. The Reissner–Nordstrom–Vaidya solution is type D whereas the Kerr–Newman–Vaidya metric is algebraically special of type II by the Petrov classification of space–time. These embedded solutions can be expressed in the Kerr–Schild ansatze on different backgrounds. The energy–momentum tensors for both nonrotating as well as rotating embedded solutions satisfy the energy conservation equations which show that they are solutions of Einstein's field equations. The surface gravity, area, temperature and entropy are also presented for each embedded black hole. It is observed that the area of the embedded black holes is greater than the sum of the areas of the individual ones. By considering the charge to be a function of radial coordinates it is shown that there is a change in the masses of the variably charged black holes. If such radiation continues, the mass of the black hole will evaporate completely thereby forming "instantaneous" charged black holes and creating embedded negative mass naked singularities describing the possible the life of radiation embedded black holes during their continuous radiation processes.

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2

IBOHAL, NG, and L. DORENDRO. "NON-STATIONARY ROTATING BLACK HOLES: ENTROPY AND HAWKING'S RADIATION." International Journal of Modern Physics D 14, no. 08 (August 2005): 1373–412. http://dx.doi.org/10.1142/s0218271805007127.

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In this paper we derive a class of non-stationary rotating solutions including Vaidya–Bonnor–de Sitter, Vaidya–Bonnor-monopole and Vaidya–Bonnor–Kerr. The rotating Viadya–Bonnor–de Sitter solution describes an embedded black hole that the rotating Vaidya–Bonnor black hole is embedded into the rotating de Sitter cosmological universe. In the case of the Vaidya–Bonnor–Kerr, the rotating Vaidya–Bonnor solution is embedded into the vacuum Kerr solution, and similarly, Vaidya–Bonnor-monopole. By considering the charge to be function of u and r, we discuss the Hawking's evaporation of the masses of variable-charged non-embedded, non-rotating and rotating Vaidya–Bonnor, and embedded rotating, Vaidya–Bonnor–de Sitter, Vaidya–Bonnor-monopole and Vaidya–Bonnor–Kerr, black holes. It is found that every electrical radiation of variable-charged black holes will produce a change in the mass of the body without affecting the Maxwell scalar in non-embedded cases; whereas in embedded cases, the Maxwell scalar, the cosmological constant, monopole charge and the Kerr mass are not affected by the radiation process. It was also found that during the Hawking's radiation process, after the complete evaporation of masses of these variable-charged black holes, the electrical radiation will continue creating (i) negative mass naked singularities in non-embedded ones, and (ii) embedded negative mass naked singularities in embedded black holes. The surface gravity, entropy and angular velocity of the horizon are presented for each of these non-stationary black holes.

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3

Mustari, Mustari, and Yuant Tiandho. "Thermodynamics of a Non-Stationary Black Hole Based on Generalized Uncertainty Principle." Journal of Physics: Theories and Applications 1, no. 2 (October 29, 2017): 127. http://dx.doi.org/10.20961/jphystheor-appl.v1i2.19308.

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In the general theory of relativity (GTR), black holes are defined as objects with very strong gravitational fields even light can not escape. Therefore, according to GTR black hole can be viewed as a non-thermodynamic object. The worldview of a black hole began to change since Hawking involves quantum field theory to study black holes and found that black holes have temperatures that analogous to black body radiation. In the theory of quantum gravity there is a term of the minimum length of an object known as the Planck length that demands a revision of Heisenberg's uncertainty principle into a Generalized Uncertainty Principle (GUP). Based on the relationship between the momentum uncertainty and the characteristic energy of the photons emitted by a black hole, the temperature and entropy of the non-stationary black hole (Vaidya-Bonner black hole) were calculated. The non-stationary black hole was chosen because it more realistic than static black holes to describe radiation phenomena. Because the black hole is dynamic then thermodynamics studies are conducted on both black hole horizons: the apparent horizon and its event horizon. The results showed that the dominant correction term of the temperature and entropy of the Vaidya-Bonner black hole are logarithmic.

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4

LIU, BAI SHENG, and JING YI ZHANG. "DISCUSSION ON EVENT HORIZON AND QUANTUM ERGOSPHERE OF DYNAMIC DE SITTER BLACK HOLES." Modern Physics Letters A 27, no. 04 (February 10, 2012): 1250010. http://dx.doi.org/10.1142/s0217732312500101.

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In the paper, the tunneling framework is applied to calculate the local horizons of Vaidya–de Sitter black holes and Vaidya–Bonner–de Sitter black holes. The researches show that the quantum ergosphere of a spherically symmetric black hole is identical with the potential barrier set by the tunneling process. The calculations also indicate that both the apparent horizons of the dynamic de Sitter black hole produce Hawking radiation. The conclusions can be applicable to either the charged or uncharged particles' Hawking radiation.

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5

CASTRO, C., J. A. NIETO, L. RUIZ, and J. SILVAS. "ON TIME-DEPENDENT BLACK HOLES AND COSMOLOGICAL MODELS FROM A KALUZA–KLEIN MECHANISM." International Journal of Modern Physics A 24, no. 07 (March 20, 2009): 1383–415. http://dx.doi.org/10.1142/s0217751x09042931.

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Novel static, time-dependent and spatial–temporal solutions to Einstein field equations, displaying singularities, with and without horizons, and in several dimensions, are found based on a dimensional reduction procedure widely used in Kaluza–Klein-type theories. The Kerr–Newman black hole entropy as well as the Reissner–Nordstrom, Kerr and Schwarzschild black hole entropy are derived from the corresponding Euclideanized actions. A very special cosmological model based on the dynamical interior geometry of a black hole is found that has no singularities at t = 0 due to the smoothing of the mass distribution. We conclude with another cosmological model equipped also with a dynamical horizon and which is related to Vaidya's metric (associated with the Hawking radiation of black holes) by interchanging t ↔ r, which might render our universe a dynamical black hole.

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6

Ishwarchandray, Ngangbam, and Ng Ibohal. "Black Holes in Non-stationary de Sitter Space with Variable Λ(u)." Journal of the Tensor Society 11, no. 01 (June 30, 2007): 25–48. http://dx.doi.org/10.56424/jts.v11i01.10586.

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In this paper we discuss a class of non-stationary solutions of Einstein’s field equations based on the non-stationary de Sitter space-time. These solutions include Schwarz-schild-de Sitter and Vaidya-de Sitter black holes with a cosmological variable Λ(u). Schwarzschild-de Sitter solution with variable Λ(u) is regarded as a generalization of Schwarzschild-de Sitter solution with constant Λ. Vaidya-de Sitter black hole with variable Λ(u) is also a generalization of the radiating Vaidya black hole embedded into the stationary de Sitter space with constant Λ. It is shown the interaction of the Vaidya null fluid with the non-stationary de Sitter field expressing in an energy-momentum tensor. The energy-momentum tensor of the embedded de Sitter black holes satisfies the energy conservation law. The energy conditions (like weak, strong and dominant conditions) for the energy-momentum tensor are also studied. The physical properties of the time-like vector fields for both the embedded solutions are discussed. It is also found that the space-time geometry of Schwarzschild-de Sitter and Vaidya-de Sitter solution with variable Λ(u) are type D in the Petrov classifications of space-times. We also discuss the surface gravity, temperature and entropy of the space-time on the cosmological black hole horizons. It is also suggested that the modified Einstein’s field equations associated with a variable cosmological Λ(u) will take the form R_{ab}−(1/2) R g_{ab}+ Λ(u) g_{ab} = −K{T_{ab}+T^(NS)_{ab} } for any type of matter field distribution T_{ab}.

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7

WU, S. Q., and X. CAI. "NON-EXISTENCE OF NEW QUANTUM ERGOSPHERE EFFECT OF A VAIDYA-TYPE BLACK HOLE." Modern Physics Letters A 16, no. 24 (August 10, 2001): 1549–57. http://dx.doi.org/10.1142/s0217732301004789.

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Hawking evaporation of Dirac particles and scalar fields in a Vaidya-type black hole is investigated by the method of generalized tortoise coordinate transformation. It is shown that Hawking radiation of Dirac particles does not exist for P1, Q2 components but for P2, Q1 components in any Vaidya-type black holes. Both the location and the temperature of the event horizon change with time. The thermal radiation spectrum of Dirac particles is the same as that of Klein–Gordon particles. We demonstrate that there is no new quantum ergosphere effect in the thermal radiation of Dirac particles in any spherically symmetry black holes.

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8

Kumah, Mohammed, and Francis T. Oduro. "On the Trapped Surface Characterization of Black Hole Region in Vaidya Spacetime." Journal of Mathematics Research 10, no. 1 (January 8, 2018): 59. http://dx.doi.org/10.5539/jmr.v10n1p59.

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Characterizing black holes by means of classical event horizon is a global concept because it depends on future null infinity. This means, to find black hole region and event horizon requires the notion of the entire spacetime which is a teleological concept. With this as a motivation, we use local approach as a complementary means of characterizing black holes. In this paper we apply Gauss divergence and covariant divergence theorems to compute the fluxes and the divergences of the appropriate null vectors in Vaidya spacetime and thus explicitly determine the existence of trapped and marginally trapped surfaces in its black hole region.

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9

Chen, Ge-Rui, and Yong-Chang Huang. "Entropy spectrum of the apparent horizon of Vaidya black holes via adiabatic invariance." Modern Physics Letters A 31, no. 06 (February 21, 2016): 1650011. http://dx.doi.org/10.1142/s0217732316500115.

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The spectroscopy of the apparent horizon of Vaidya black holes is investigated via adiabatic invariance. We obtain an equally spaced entropy spectrum with its quantum equal to the one given by Bekenstein [J. D. Bekenstein, Phys. Rev. D 7, 2333 (1973)]. We demonstrate that the quantization of entropy and area is a generic property of horizon, not only for stationary black holes, and the results also exit in a dynamical black hole. Our work also shows that the quantization of black hole is closely related to the tunneling formalism for deriving the Hawking effect, which is interesting.

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10

Sadeghian, S., and A. Shafiekhani. "Extremal charged Vaidya and its near horizon geometry." International Journal of Modern Physics D 26, no. 04 (February 17, 2017): 1750036. http://dx.doi.org/10.1142/s0218271817500365.

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Recently [Formula: see text]-dimensional spherically symmetric charged Vaidya black hole solution has been constructed. We observe that this nonstationary solution admits extremal limit and study its near horizon geometry. We show that the symmetry of the near horizon geometry is [Formula: see text]. Our analysis shows that the theorems for the near horizon geometry of stationary extremal black holes, may be extended to nonstationary cases.

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11

Salimi, Ahmad H., and Triyanta. "The Semiclassical Methods for Hawking Radiations on the Kerr – Newman – Vaidya Black Holes." Journal of Physics: Conference Series 2243, no. 1 (June 1, 2022): 012099. http://dx.doi.org/10.1088/1742-6596/2243/1/012099.

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Abstract Hawking radiation can be described as particle tunnelling picture in semiclassical regime. In this research, we derived Hawking temperature and entropy of non-stationary black hole Kerr - Newman - Vaidya using two semiclassical methods, which are radial null geodesic and complex path analysis. These two calculations gave the same results. The Hawking temperature is, approximately, inversely proportional to the mass and non-stationary term. We also derived the entropy of the black hole that corresponds to the temperature formulations that were derived by semiclassical methods. The entropy formulations that were calculated obey generalized second law of black holes.

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12

REN, JI-RONG, and RAN LI. "UNIFIED FIRST LAW AND THERMODYNAMICS OF DYNAMICAL BLACK HOLE IN n-DIMENSIONAL VAIDYA SPACETIME." Modern Physics Letters A 23, no. 38 (December 14, 2008): 3265–70. http://dx.doi.org/10.1142/s0217732308028831.

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As a simple but important example of dynamical black hole, we analyze the dynamical black hole in n-dimensional Vaidya spacetime in detail. We investigated the thermodynamics of field equation in n-dimensional Vaidya spacetime. The unified first law was derived in terms of the methods proposed by Hayward. The first law of dynamical black hole was obtained by projecting the unified first law along the trapping horizon. The second law of dynamical black hole is also discussed.

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13

Liu, Xianming, and Wenbiao Liu. "Fluctuation on a Schwarzschild black hole." Canadian Journal of Physics 87, no. 9 (September 2009): 1009–12. http://dx.doi.org/10.1139/p09-068.

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When a relativistic perturbation is given to the horizon of a Schwarzschild black hole, a new supersurface near the horizon will be obtained. Using the gravitational anomaly method proposed by Robinson and Wilczek, Hawking radiation from this new supersurface is calculated. It is found that the first law of thermodynamics can also be constructed successfully on this supersurface. The expressions of the characteristic position and temperature are very similar to the previous results for the event horizon of a Vaidya black hole. Comparing with the Vaidya black hole, we conclude that Hawking radiation and the thermodynamics of a Vaidya black hole should be indeed constructed at the apparent horizon instead of the event horizon.

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14

SIAHAAN, HARYANTO M., and TRIYANTA. "SEMICLASSICAL METHODS FOR HAWKING RADIATION FROM A VAIDYA BLACK HOLE." International Journal of Modern Physics A 25, no. 01 (January 10, 2010): 145–53. http://dx.doi.org/10.1142/s0217751x1004749x.

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We derive the general form of Hawking temperature for Vaidya black hole in the tunneling pictures. This type of black hole is regarded as the description of a more realistic one compared to static case such as Schwarzschild's solution. The black hole mass in Vaidya solution is time dependent and decreasing due to evaporation process. Clearly, the temperature would be time dependent as our findings show. We use the semiclassical methods, namely radial null geodesic and complex paths methods. Both methods are found to give the same results. Then, we discuss the possible form of the corresponding entropy.

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15

KE-XIA, JIANG, KE SAN-MIN, and PENG DAN-TAO. "HAWKING RADIATION AS TUNNELING AND THE UNIFIED FIRST LAW OF THERMODYNAMICS FOR A CLASS OF DYNAMICAL BLACK HOLES." International Journal of Modern Physics D 18, no. 11 (November 15, 2009): 1707–17. http://dx.doi.org/10.1142/s0218271809015254.

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An analysis is made for relations between the tunneling rate and the unified first law of thermodynamics at the trapping horizons of two kinds of spherically symmetric dynamical black holes. The first kind is the Vaidya–Bardeen black hole; the tunneling rate Γ ~ e△S can be obtained naturally from the unified first law at the apparent horizon, which holds the form dEH = TdS + WdV. The second kind is the McVittie solution; the action of the radial null geodesic of the outgoing particles does not always have a pole at the apparent horizon, while the ingoing mode always has one. The solution of the ingoing mode of the radiation can be mathematically reduced to the case in the FRW universe smoothly. However, as a black hole, the physical meaning is unclear and even puzzling.

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16

Mehdipour, S. Hamid. "Gravitational energy of a noncommutative Vaidya black hole." Canadian Journal of Physics 91, no. 3 (March 2013): 242–45. http://dx.doi.org/10.1139/cjp-2012-0485.

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In this paper we evaluate the components of the energy–momentum pseudotensors of Landau and Lifshitz for the noncommutative Vaidya space–time. The effective gravitational mass experienced by a neutral test particle present at any finite distance in the gravitational field of the noncommutative Vaidya black hole is derived. Using the effective mass parameter, one finds that the naked singularity is massless and this supports Seifert's conjecture.

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17

Qi, De-Jiang, Wei-Min Wang, and Shuang-Mei Li. "Fermion tunneling effect in Vaidya-de Sitter space." Canadian Journal of Physics 88, no. 4 (April 2010): 277–82. http://dx.doi.org/10.1139/p10-026.

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In this paper, by considering energy conservation and the self-gravitation reaction in the dynamical background space-time, we attempt to extend Kerner and Mann's work to the Vaidya–de Sitter black hole by the fermion-tunneling method. The result we derive shows that the tunneling probability of the Vaidya–de Sitter black hole is related not only to the change in the Bekenstein–Hawking entropy but also to the integral of the changing horizon, which are different from the stationary cases.

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18

Li, Hui-Ling, Shu-Zheng Yang, Teng-Jiao Zhou, and Rong Lin. "Fermion tunneling from a Vaidya black hole." EPL (Europhysics Letters) 84, no. 2 (October 2008): 20003. http://dx.doi.org/10.1209/0295-5075/84/20003.

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19

Farley, A. N. St J., and P. D. D'Eath. "Vaidya Space-Time in Black-Hole Evaporation." General Relativity and Gravitation 38, no. 3 (February 7, 2006): 425–43. http://dx.doi.org/10.1007/s10714-006-0231-3.

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20

Chang-Jun, Gao, and Shen You-Gen. "Fermion Entropy of Vaidya-Bonner Black Hole." Chinese Physics Letters 18, no. 9 (August 16, 2001): 1167–69. http://dx.doi.org/10.1088/0256-307x/18/9/304.

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21

Kim, Sung-Won, Eun-Young Choi, Sung Ku Kim, and Jongmann Yang. "Black hole radiation in the Vaidya metric." Physics Letters A 141, no. 5-6 (November 1989): 238–42. http://dx.doi.org/10.1016/0375-9601(89)90477-5.

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22

POLLOCK, M. D. "ON THE QUANTIZATION OF CHARGED BLACK HOLES." International Journal of Modern Physics D 07, no. 04 (August 1998): 521–34. http://dx.doi.org/10.1142/s0218271898000358.

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The Wheeler–DeWitt equation for the wave function Ψ of the Schwarzschild black hole has been derived by Tomimatsu in the form of a Schrödinger equation, valid on the apparent horizon, using the two-dimensional Hamiltonian formalism of Hajicek and the radiating Vaidya metric. Here, the analysis is generalized to the Reissner–Nordström black hole. At constant charge Q, the evaporation rate is calculated from the solution for Ψ to be [Formula: see text], where k is a constant and [Formula: see text] are the radii of the outer event horizon and inner Cauchy horizon. In the extremal limit M → Q, however, the Hawking temperature [Formula: see text] tends to zero, suggesting, when the back reaction is taken into account, that the evaporation cannot occur this way and in agreement with the known discharging process of the hole via the Schwinger electron–positron pair-production mechanism. The more general charged dilaton black holes obtained from the theory L4 = [R4 - 2 (∇ Φ)2 - e-2aΦF2 ]/16π are also discussed, and it is explained why this quantization procedure cannot be applied when a is non-zero.

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23

Vertogradov, Vitalii. "Gravitational collapse of Vaidya spacetime." International Journal of Modern Physics: Conference Series 41 (January 2016): 1660124. http://dx.doi.org/10.1142/s2010194516601241.

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The gravitational collapse of generalized Vaidya spacetime is considered. It is known that the endstate of gravitational collapse, as to whether a black hole or a naked singularity is formed, depends on the mass function [Formula: see text]. Here we give conditions for the mass function which corresponds to the equation of the state [Formula: see text] where [Formula: see text] and according to these conditions we obtain either a black hole or a naked singularity at the endstate of gravitational collapse. Also we give conditions for the mass function when the singularity is gravitationally strong.

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24

NAYERI, ALI. "BRANE COSMOLOGY WITH NON-STATIC BULK." International Journal of Modern Physics A 16, supp01c (September 2001): 1040–42. http://dx.doi.org/10.1142/s0217751x01008837.

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We study the brane world motion in non-static bulk by generalizing the second Randall-Sundrum scenario Explicitly, we take the bulk to be a Vaidya-AdS metric, which describes the gravitational collapse of a spherically symmetric null dust fluid in Anti-de Sitter spacetime. We point out that during an inflationary phase on the brane, black holes will tend to be thermally nucleated in the bulk We analyze the thermodynamical properties of this brane-world. We point out that during an inflationary phase on the brane, black holes will tend to be thermally nucleated in the bulk. Thermal equilibrium of the system is discussed. We calculate the late time behavior of this system, including 1-loop effects. We argue that at late times a sufficiently large black hole will relax to a point of thermal equilibrium with the brane-world environment. This result has interesting implications for early-universe cosmology.

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25

Tiandho, Yuant. "MESIN PANAS FOTO-CARNOT LUBANG HITAM NON-STASIONER." Jurnal Sains Dasar 6, no. 1 (May 22, 2017): 17. http://dx.doi.org/10.21831/jsd.v6i1.13065.

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Di dalam makalah ini disajikan suatu analisis teoritik dari desain mesin panas foto-Carnot dengan sumber energi berupa lubang hitam non-stasioner. Diharapkan dari kajian ini dapat diketahui potensi penggunaan lubang hitam sebagai sumber “bahan bakar” dari suatu mesin panas. Desain mesin panas berbasis lubang hitam dikembangkan karena melalui mekanika kuantum lubang hitam dapat mengemisikan partikel dan memiliki temperatur layaknya dalam proses radiasi benda hitam. Perhitungan temperatur lubang hitam non-stasioner yang meradiasikan foton dilakukan berdasarkan gambaran tunneling dengan menggunakan metode Hamilton-Jacobi. Sebagai hasilnya, lubang hitam non-stasioner memiliki temperatur yang juga bergantung terhadap laju perubahan massa. Desain mesin panas yang dikaji dalam makalah ini terdiri dari dua buah lubang hitam non-stasioner berbeda massa sehingga memiliki perbedaan tekanan radiasi yang dapat menggerakkan piston. Secara umum, efisiensi dari mesin foto-Carnot bergantung pada massa lubang hitam, laju perubahan massa, serta suatu fungsi penyeimbang dalam metrik Vaidya.Kata kunci: mesin foto-Carnot, termodinamika lubang hitam, non-stasioner. Non-Stationary Black Hole Photo-Carnot Heat Engine Abstract This paper presents a theoretical analysis of a photo-Carnot heat engine design with an energy source from a non-stationary black hole. This study may provide a clue about the potential use of black hole as a “fuel” of a heat engine. Heat engine design was developed because according to quantum mechanics a black hole may emit particles and it has temperature like in the black-body radiation. The calculation of non-stationary black hole temperature which radiate photons is based on the tunneling picture by using the Hamilton-Jacobi method. As a result, the temperature of non-stationary black hole also depends on the mass flow rate. The model of heat engine that studied in this work contains two non-stationary black holes with different masses that have different radiation pressure to move the piston. In general, the efficiency of photo-Carnot engine depend on the mass of the black hole, the mass flow rate, and the balance function in the Vaidya metric. Keywords: photo-Carnot engine, black hole thermodynamics, non-stationary.

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26

Lin Kai and Yang Shu-Zheng. "Fermions tunneling of the Vaidya-Bonner black hole." Acta Physica Sinica 58, no. 2 (2009): 744. http://dx.doi.org/10.7498/aps.58.744.

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Jing-Yi, Zhang, and Zhao Zheng. "New Coordinates for the Evaporating Vaidya Black Hole." Chinese Physics Letters 23, no. 5 (April 28, 2006): 1099–102. http://dx.doi.org/10.1088/0256-307x/23/5/010.

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28

Xiang, Li, and You-Gen Shen. "Letter: Gravitational Thermodynamics of a Vaidya Black Hole." General Relativity and Gravitation 36, no. 6 (June 2004): 1473–81. http://dx.doi.org/10.1023/b:gerg.0000022583.50544.da.

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29

Biernacki, Waldemar. "Evaporating black hole in a Vaidya space-time." Physical Review D 41, no. 4 (February 15, 1990): 1356–57. http://dx.doi.org/10.1103/physrevd.41.1356.

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Li, Zhong-heng. "Vaidya-de Sitter Black Hole with Spin Fields." Chinese Physics Letters 15, no. 8 (August 1, 1998): 553–54. http://dx.doi.org/10.1088/0256-307x/15/8/003.

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LIU, XIANMING, ZHENG ZHAO, and WENBIAO LIU. "TORTOISE COORDINATE TRANSFORMATION ON APPARENT HORIZON OF A DYNAMICAL BLACK HOLE." International Journal of Modern Physics: Conference Series 12 (January 2012): 358–67. http://dx.doi.org/10.1142/s2010194512006563.

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Thinking of Hawking radiation calculation from a Schwarzschild black hole using Damour-Ruffini method, some key requirements of the tortoise coordinate transformation are pointed out. Extending these requirements to a dynamical black hole, a dynamical tortoise coordinate transformation is proposed. Under this new dynamical tortoise coordinate transformation, Hawking radiation from a Vaidya black hole can be got successfully using Damour-Ruffini method. Moreover, we also find that the radiation should be regarded as originating from the apparent horizon rather than the event horizon at least from the viewpoint of the first law of thermodynamics.

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32

XIANG, LI, and ZHAO ZHENG. "ENTROPY OF A NONSTATIC BLACK HOLE." Modern Physics Letters A 15, no. 28 (September 14, 2000): 1739–47. http://dx.doi.org/10.1142/s0217732300001973.

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We point out that the brick-wall model cannot be applied to the nonstatic black hole. In the case of a static hole, we propose a new model where the black hole entropy is attributed to the dynamical degrees of the field covering the two-dimensional membrane just outside the horizon. A cutoff different from the model of 't Hooft is necessarily introduced. It can be treated as an increase in horizon because of the space–time fluctuations. We also apply our model to the nonequilibrium and nonstatic cases, such as Schwarzschild–de Sitter and Vaidya space–times. In the nonstatic case, the entropy relies on a time-dependent cutoff.

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33

Chen, Ge-Rui, and Yong-Chang Huang. "Hawking radiation of vector particles as tunneling from the apparent horizon of Vaidya black holes." International Journal of Modern Physics A 30, no. 15 (May 26, 2015): 1550083. http://dx.doi.org/10.1142/s0217751x15500839.

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Vector particles' Hawking radiation as tunneling from the apparent horizon of Vaidya black holes is investigated. By applying the WKB approximation and the appropriate ansatz for the form of the action to the Proca equation, we obtain the tunneling spectrum of vector particles. As a result, the expected Hawking temperature is recovered by vector particles tunneling from the apparent horizon of Vaidya black holes.

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34

Zhang, Jie, Zhie Liu, Bei Sha, Xia Tan, Yuzhen Liu, and Shuzheng Yang. "Influence of Lorentz Invariation Violation on Arbitrary Spin Fermion Tunneling Radiation in the Vaidya-Bonner Space-Time." Advances in High Energy Physics 2020 (March 18, 2020): 1–6. http://dx.doi.org/10.1155/2020/2742091.

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In the space-time of the nonstationary spherical symmetry Vaidya-Bonner black hole, an accurate modification of Hawking tunneling radiation for fermions with arbitrary spin is researched. Considering a light dispersion relationship derived from string theory, quantum gravitational theory, and the Rarita-Schwinger equation in the nonstationary spherical symmetry space-time, we derive an accurately modified dynamic equation for fermions with arbitrary spin. By solving the equation, the modified tunneling rate of fermions with arbitrary spin, Hawking temperature, and entropy at the event horizon of the Vaidya-Bonner black hole are presented. We find that the Hawking temperature will increase, but the entropy will decrease compared with the case without the Lorentz Invariation Violation modification.

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35

Lin, Kai. "Nonequilibrium Black Hole Thermodynamics in Anti-de Sitter Spacetime." Advances in High Energy Physics 2021 (December 28, 2021): 1–5. http://dx.doi.org/10.1155/2021/4613870.

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This work discusses the black hole thermodynamics in a weak dynamical Anti-de Sitter spacetime, which should be described by the nonequilibrium thermodynamics, because the metric depends on the time coordinate. Taking the Vaidya-Anti-de Sitter black hole spacetime as an example, the local entropy balance equations and principle of minimum entropy generation are derived, and finally, some irreversible effects in nonequilibrium thermodynamics are studied by using the Onsager reciprocal relation.

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36

POLLOCK, M. D. "ON THE WHEELER-DEWITT EQUATION FOR BLACK HOLES." International Journal of Modern Physics D 03, no. 03 (September 1994): 579–91. http://dx.doi.org/10.1142/s0218271894000721.

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Integration over the angular coordinates of the evaporating, four-dimensional Schwarzschild black hole leads to a two-dimensional action, for which the Wheeler-DeWitt equation has been found by Tomimatsu, on the apparent horizon, where the Vaidya metric is valid, using the Hamiltonian formalism of Hajicek. For the Einstein theory of gravity coupled to a massless scalar field ζ, the wave function Ψ obeys the Schrödinger equation [Formula: see text], where M is the mass of the hole. The solution is [Formula: see text], where k2 is the separation constant, and for k2>0 the hole evaporates at the rate Ṁ=−k2/4M2, in agreement with the result of Hawking. Here, this analysis is generalized to the two-dimensional theory [Formula: see text], which subsumes the spherical black holes formulated in D≥4 dimensions, when A = ½ (D - 2) (D - 3)ϕ2 (D - 4)/(D - 2), B=2(D−3)/(D−2), C=1, and also the twodimensional black hole identified by Witten and by Gautam et al., when A=4/α′, B=2, C=1/8π, c=+8/α′ being (minus) the central charge. In all cases an analogous Schrödinger equation is obtained. The evaporation rate is [Formula: see text] when D≥4 and [Formula: see text] when D=2. Since Ψ evolves without violation of unitarity, there is no loss of information during the evaporation process, in accord with the principle of black-hole complementarity introduced by Susskind et al. Finally, comparison with the four-dimensional, cosmological Schrödinger equation, obtained by reduction of the ten-dimensional heterotic superstring theory including terms [Formula: see text], shows in both cases that there is a positive semi-definite potential which evolves to zero, this corresponding to the ground state, which is Minkowski space.

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37

Vertogradov, Vitalii, and Maxim Misyura. "Vaidya and Generalized Vaidya Solutions by Gravitational Decoupling." Universe 8, no. 11 (October 27, 2022): 567. http://dx.doi.org/10.3390/universe8110567.

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In this paper, we apply the gravitational decoupling method for dynamical systems in order to obtain a new type of solution that can describe a hairy dynamical black hole. We consider three cases of decoupling. The first one is the simplest and most well known when the mass function is the function only of space coordinate r. The second case is a Vaidya spacetime case when the mass function depends on time v . Finally, the third case represents the generalization of these two cases: the mass function is the function of both r and v. We also calculate the apparent horizon and singularity locations for all three cases.

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38

Shi Wang-Lin, Liu Xing-Ye, and Liu Zhen-Xing. "Dirac radiation of Vaidya-Bonner-de Sitter black hole." Acta Physica Sinica 53, no. 7 (2004): 2396. http://dx.doi.org/10.7498/aps.53.2396.

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39

Bowaire, Anike N. "Hawking Temperature of the Reissner-Nordstrom-Vaidya Black Hole." Journal of Mathematical and Fundamental Sciences 45, no. 2 (July 2013): 114–23. http://dx.doi.org/10.5614/j.math.fund.sci.2013.45.2.2.

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40

Jun, Ren, and Zhao Zheng. "Tunnelling effect from a Vaidya–de Sitter black hole." Chinese Physics 15, no. 2 (January 16, 2006): 292–95. http://dx.doi.org/10.1088/1009-1963/15/2/009.

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41

Li, Zhongheng, and Zheng Zhao. "Thermal Radiation of Dirac Particles from Vaidya Black Hole." Chinese Physics Letters 10, no. 2 (February 1993): 126–28. http://dx.doi.org/10.1088/0256-307x/10/2/018.

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42

Tiandho, Yuant, and Triyanta. "Dirac Particles Emission from Reissner-Nordstrom-Vaidya Black Hole." Journal of Physics: Conference Series 739 (August 2016): 012146. http://dx.doi.org/10.1088/1742-6596/739/1/012146.

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43

Sharif, M., and W. Javed. "Black hole evaporation in a noncommutative charged Vaidya model." Journal of Experimental and Theoretical Physics 114, no. 6 (June 2012): 933–45. http://dx.doi.org/10.1134/s1063776112050123.

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44

MOLINA, ALFRED, and NARESH DADHICH. "ON KALUZA–KLEIN SPACE–TIME IN EINSTEIN–GAUSS–BONNET GRAVITY." International Journal of Modern Physics D 18, no. 04 (April 2009): 599–611. http://dx.doi.org/10.1142/s0218271809014650.

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By considering the product of the usual four-dimensional space–time with two dimensional space of constant curvature, an interesting black hole solution has recently been found for Einstein–Gauss–Bonnet gravity. It turns out that this as well as all others could easily be made to radiate Vaidya null dust. However, there exists no Kerr analog in this setting. To get the physical feel of the four-dimensional black hole space–times, we study asymptotic behavior of stresses at the two ends, r → 0 and r → ∞.

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KAI, LIN, and YANG SHUZHENG. "FERMIONS TUNNELING FROM BARDEEN–VAIDYA BLACK HOLE VIA GENERAL TORTOISE COORDINATE TRANSFORMATION." Modern Physics Letters A 24, no. 22 (July 20, 2009): 1775–83. http://dx.doi.org/10.1142/s0217732309030254.

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In this paper, we research on the scalar field particles and 1/2 spin fermions tunneling from the event horizon of Bardeen–Vaidya black hole by semiclassical method and general tortoise coordinate transformation, and obtain the Hawking temperature and tunneling rate near the event horizon.

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46

Jing-Yi, Zhang, Zhang Jing-Yi, and Zhao Zheng. "Tunnelling Effect and Hawking Radiation from a Vaidya Black Hole." Chinese Physics Letters 23, no. 8 (July 21, 2006): 2019–22. http://dx.doi.org/10.1088/0256-307x/23/8/016.

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47

Chen, Deyou, and Shuzheng Yang. "Hawking radiation of the Vaidya–Bonner–de Sitter black hole." New Journal of Physics 9, no. 8 (August 2, 2007): 252. http://dx.doi.org/10.1088/1367-2630/9/8/252.

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Yang, ShuZheng, and DeYou Chen. "Hawking Radiation as Tunneling from the Vaidya–Bonner Black Hole." International Journal of Theoretical Physics 46, no. 11 (May 30, 2007): 2923–27. http://dx.doi.org/10.1007/s10773-007-9404-4.

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49

Zhang, Yongping, and Wenbiao Liu. "Back reaction and Hawking radiation from a Vaidya black hole." Astrophysics and Space Science 312, no. 3-4 (November 3, 2007): 315–19. http://dx.doi.org/10.1007/s10509-007-9696-0.

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50

Niu, Zhen-Feng, and Wen-Biao Liu. "Hawking radiation and thermodynamics of a Vaidya–Bonner black hole." Research in Astronomy and Astrophysics 10, no. 1 (January 2010): 33–38. http://dx.doi.org/10.1088/1674-4527/10/1/003.

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