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Journal articles on the topic 'Schwarzschild space'

Author: Grafiati

Published: 4 June 2025

Last updated: 15 July 2025

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1

Austin, Rickey W. "Discrete Space-Time on the Manifestation of Mass." European Scientific Journal, ESJ 14, no. 3 (2018): 31. http://dx.doi.org/10.19044/esj.2018.v14n3p31.

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Schwarzschild’s Metric (Schwarzschild 1916) under specific conditions provides a Taylor series first order discrete length when transforming coordinates between observers. Exploring the consequences of the discrete length produces an a priori result of quantized space-time. Deriving base units from the quantization of space-time and applying elementary charge, exact formulations for the observed Schwarzschild’s discrete units are obtained. These units are equivalent to Planck’s mass, length, time, momentum, force, energy and Planck’s constant (NIST CODATA 2014).

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2

MONTE, EDMUNDO M. "WHAT IS THE TOPOLOGY OF A SCHWARZSCHILD BLACK HOLE?" International Journal of Modern Physics: Conference Series 18 (January 2012): 125–29. http://dx.doi.org/10.1142/s201019451200832x.

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We investigate the topology of Schwarzschild's black holes through the immersion of this space-time in space of higher dimension. Through the immersions of Kasner and Fronsdal we calculate the extension of the Schwarzschilds black hole.

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3

GARATTINI, REMO. "SPACE TIME FOAM." International Journal of Modern Physics A 17, no. 06n07 (2002): 829–32. http://dx.doi.org/10.1142/s0217751x02010200.

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In the context of a model of space-time foam, made by N wormholes we discuss the possibility of having a foam formed by different configurations. An equivalence between Schwarzschild and Schwarzschild-Anti-de Sitter wormholes in terms of Casimir energy is shown. An argument to discriminate which configuration could represent a foamy vacuum coming from Schwarzschild black hole transition frequencies is used. The case of a positive cosmological constant is also discussed. Finally, a discussion involving charged wormholes leads to the conclusion that they cannot be used to represent a ground state of the foamy type.

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4

Gen, Uchida, and Tetsuya Shiromizu. "Asymptotically Schwarzschild space–times." Journal of Mathematical Physics 40, no. 4 (1999): 2021–31. http://dx.doi.org/10.1063/1.532848.

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5

Porter, John R. "The Schwarzschild H space." General Relativity and Gravitation 17, no. 2 (1985): 179–86. http://dx.doi.org/10.1007/bf00760530.

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6

Kruglov, S. I. "Black hole emission of vector particles in (1+1) dimensions." International Journal of Modern Physics A 29, no. 22 (2014): 1450118. http://dx.doi.org/10.1142/s0217751x14501188.

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We investigate the radiation of spin-1 particles by black holes in (1+1) dimensions within the Proca equation. The process is considered as quantum tunneling of bosons through an event horizon. It is shown that the emission temperature for the Schwarzschild background geometry is the same as the Hawking temperature corresponding to scalar particles emission. We also obtain the radiation temperatures for the de Sitter, Rindler and Schwarzschild–de Sitter space–times. In a particular case when two horizons in Schwarzschild–de Sitter space–time coincides, the Nariai temperature is recovered. The thermodynamical entropy of a black hole is calculated for Schwarzschild–de Sitter space–time having two horizons.

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7

Mason, Lionel J., and Jean-Philippe Nicolas. "Regularity at space-like and null infinity." Journal of the Institute of Mathematics of Jussieu 8, no. 1 (2008): 179–208. http://dx.doi.org/10.1017/s1474748008000297.

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AbstractWe extend Penrose's peeling model for the asymptotic behaviour of solutions to the scalar wave equation at null infinity on asymptotically flat backgrounds, which is well understood for flat space-time, to Schwarzschild and the asymptotically simple space-times of Corvino–Schoen/Chrusciel–Delay. We combine conformal techniques and vector field methods: a naive adaptation of the ‘Morawetz vector field’ to a conformal rescaling of the Schwarzschild metric yields a complete scattering theory on Corvino–Schoen/Chrusciel–Delay space-times. A good classification of solutions that peel arises from the use of a null vector field that is transverse to null infinity to raise the regularity in the estimates. We obtain a new characterization of solutions admitting a peeling at a given order that is valid for both Schwarzschild and Minkowski space-times. On flat space-time, this allows larger classes of solutions than the characterizations used since Penrose's work. Our results establish the validity of the peeling model at all orders for the scalar wave equation on the Schwarzschild metric and on the corresponding Corvino–Schoen/Chrusciel–Delay space-times.

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8

OGUSHI, SACHIKO. "HOLOGRAPHIC ENTROPY ON THE BRANE IN de SITTER SCHWARZSCHILD SPACE." Modern Physics Letters A 17, no. 01 (2002): 51–58. http://dx.doi.org/10.1142/s0217732302006084.

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The relationship between the entropy of de Sitter (dS) Schwarzschild space and that of the CFT, which lives on the brane, is discussed by using Friedmann–Robertson–Walker (FRW) equations and Cardy–Verlinde formula. The cosmological constant appears on the brane with time-like metric in dS Schwarzschild background. On the other hand, in case of the brane with space-like metric in dS Schwarzschild background, the cosmological constant of the brane does not appear because we can choose brane tension to cancel it. We show that when the brane crosses the horizon of dS Schwarzschild black hole, both for time-like and space-like cases, the entropy of the CFT exactly agrees with the black hole entropy of five-dimensional dS background as it happens in the AdS/CFT correspondence.

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9

SETARE, M. R. "SPACE NONCOMMUTATIVITY CORRECTIONS TO THE CARDY–VERLINDE FORMULA." International Journal of Modern Physics A 21, no. 13n14 (2006): 3007–13. http://dx.doi.org/10.1142/s0217751x06030965.

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In this paper we compute the corrections to the Cardy–Verlinde formula of Schwarzschild black holes. These corrections stem from the space noncommutativity. Because the Schwarzschild black holes are nonrotating, to the first order of perturbative calculations, there is no any effect on the properties of black hole due to the noncommutativity of space.

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10

Keane, A. J., R. K. Barrett, and J. F. L. Simmons. "Radiative acceleration in Schwarzschild space-times." Monthly Notices of the Royal Astronomical Society 321, no. 4 (2001): 661–77. http://dx.doi.org/10.1046/j.1365-8711.2001.04014.x.

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11

Puchades, Neus, and Diego Sáez. "Relativistic positioning in Schwarzschild space-time." Journal of Physics: Conference Series 600 (April 28, 2015): 012054. http://dx.doi.org/10.1088/1742-6596/600/1/012054.

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12

Li, Xiaoyan. "Spherical Symmetric Solutions for the Motion of Relativistic Membranes in the Schwarzschild-Anti de Sitter Space-Time." Journal of Applied Mathematics 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/215018.

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This paper concerns motion of relativistic membranes in the Schwarzschild-anti de Sitter space-time. We derive a nonlinear equation for relativistic membranes moving in the Schwarzschild-anti de Sitter space-time, discuss spherical symmetric solutions for the motion equations, and obtain some interesting physical results.

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13

Witzany, Vojtěch, and Claus Lämmerzahl. "A pseudo-Newtonian description of any stationary space-time." Proceedings of the International Astronomical Union 12, S324 (2016): 45–46. http://dx.doi.org/10.1017/s1743921317000035.

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AbstractSince the first investigations into accretion onto black holes, astrophysicists have proposed effective Newtonian-like potentials to mimic the strong-field behavior of matter near a Schwarzschild or Kerr black hole. On the other hand, the fields of neutron stars or black holes in many of the alternative gravity theories differ from the idealized Schwarzschild or Kerr field which would require a number of new potentials. To resolve this, we give a Newtonian-like Hamiltonian which almost perfectly mimics the behavior of test particles in any given stationary space-time. The properties of the Hamiltonian are excellent in static space-times such as the Schwarzschild black hole, but become worse for space-times with gravito-magnetic or dragging effects such as near the Kerr black hole.

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14

GARATTINI, R. "WORMHOLES AND SPACE–TIME FOAM: THE CASE WITH A COSMOLOGICAL CONSTANT." International Journal of Modern Physics A 17, no. 20 (2002): 2760. http://dx.doi.org/10.1142/s0217751x02011874.

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We consider the computation of the energy difference between spaces having the same asymptotic behavior. Following the example of the Schwarzschild case which asymptotically tends to flat space1,2, we consider the case of a cosmological constant. The analysis is realized by means of variational methods in a Hamiltonian formulation and it is restricted to transverse-traceless (TT) tensors to one loop approximation. In particular, we consider the Schwarzschild-Anti-de Sitter (S-AdS) case which asymptotically tends to the Anti-de Sitter space and the Schwarzschild-de Sitter (SdS) case which asymptotically tends to the de Sitter space3,4. In both cases (S-AdS, SdS), we discover the existence of an unstable mode at zero temperature. This result leads to consider a different vacuum space which differs in a case to case. The configuration is stabilized by allowing N copies of the same initial system to contribute to the final energy5. A selection rule for different scenarios of a foam-like space can be given in terms of transition frequencies of the emitted radiation of a black hole6.

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15

KRAUSE, AXEL. "BLACK HOLES, SPACE-FILLING CHAINS AND RANDOM WALKS." International Journal of Modern Physics A 21, no. 28n29 (2006): 5793–806. http://dx.doi.org/10.1142/s0217751x06033982.

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Many approaches to a semiclassical description of gravity lead to an integer black hole entropy. In four dimensions this implies that the Schwarzschild radius obeys a formula which describes the distance covered by a Brownian random walk. For the higher-dimensional Schwarzschild–Tangherlini black hole, its radius relates similarly to a fractional Brownian walk. We propose a possible microscopic explanation for these random walk structures based on microscopic chains which fill the interior of the black hole.

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16

Kelekçi, Özgür. "Kähler Magnetic Curves in Conformally Euclidean Schwarzschild Space." Cumhuriyet Science Journal 45, no. 1 (2024): 147–52. http://dx.doi.org/10.17776/csj.1400543.

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In this paper, we study the magnetic curves on a Kähler manifold which is conformally equivalent to Euclidean Schwarzschild space. We show that Euclidean Schwarzschild space is locally conformally Kähler and transform it into a Kähler space by applying a conformal factor coming from its Lee form. We solve Lorentz equation to find analytical expressions for magnetic curves which are compatible with the almost complex structure of the proposed Kähler manifold. We also calculate the energy of magnetic curves.

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17

KIM, YONG-WAN, JAEDONG CHOI, and YOUNG-JAI PARK. "LOCAL FREE-FALL TEMPERATURE OF A RN–AdS BLACK HOLE." International Journal of Modern Physics A 25, no. 15 (2010): 3107–20. http://dx.doi.org/10.1142/s0217751x10049311.

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We use the global embedding Minkowski space geometries of a (3+1)-dimensional curved Reissner–Nordström (RN)–AdS black hole space–time into a (5+2)-dimensional flat space–time to define a proper local temperature, which remains finite at the event horizon, for freely falling observers outside a static black hole. Our extended results include the known limiting cases of the RN, Schwarzschild–AdS and Schwarzschild black holes.

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18

He, Chun-Lei, Shou-Jun Huang, and De-Xing Kong. "Global existence of smooth solutions to relativistic string equations in Schwarzschild space-time for small initial data." Journal of Hyperbolic Differential Equations 13, no. 01 (2016): 181–213. http://dx.doi.org/10.1142/s0219891616500053.

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This paper is concerned with the motion of relativistic strings in Schwarzschild space-time. In a general framework, we first analyze the basic equations for the motion of a [Formula: see text]-dimensional extended object in a general enveloping space-time [Formula: see text], which is a given Lorentzian manifold, and then we investigate some important properties enjoyed by the equations for the motion of relativistic strings in Schwarzschild space-time. In particular, the equations are shown to form a totally linearly degenerate system of first-order hyperbolic equations in [Formula: see text] dimensions. Based on this observation and under suitable assumptions, we are able to prove the global existence of smooth solutions to the Cauchy problem for the equations of motion of relativistic strings (in Schwarzschild space-time) with sufficiently small arc length.

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19

Yefremov, Alexander P. "Modified Gravity and a Space Probe–Venus Mission." Astronomy 1, no. 3 (2022): 246–54. http://dx.doi.org/10.3390/astronomy1030014.

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A comparison of gravitational forces and a space probe’s trajectory parameters is made for two different models of the sun’s field, expressed in Schwarzschild and isotropic coordinates. It is shown that these two representations of a single Schwarzschild solution give, in the tangent space format, different deflections from classical finite trajectories and, hence, from one other; greatly amplified by a planet’s (Venus’) gravity assist, this effect renders it possible to experimentally specify the format of the gravity law that dominates the solar system.

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20

Bendjoudi, Ahmida, and Noureddine Mebarki. "Loop gravity and Schwarzschild spacetime." International Journal of Geometric Methods in Modern Physics 14, no. 04 (2017): 1750055. http://dx.doi.org/10.1142/s0219887817500554.

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A discretization for the Schwarzschild spacetime manifold is introduced and investigated. It is shown that the discreteness of the area of space shown in loop gravity leads to a tetrahedral structure characterizing the Schwarzschild manifold.

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21

Thang, Bui Quyet, and Do Thi Huong. "A Spherically Symmetric Solution of \(R+\lambda R^2\) Gravity." Communications in Physics 24, no. 3S2 (2014): 23–28. http://dx.doi.org/10.15625/0868-3166/24/3s2/4991.

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We shortly review the metric formalism for the \(f(R)\) gravity. Based on the metric formalism, westudy the spherically symmetric static empty space solutions with the gravity Lagrangian\(L=R+\lambda R^2\). We found the general metric that described the static empty space with thespherically symmetry. Our result is more general than Schwarzschild solution, specially thepredicted metric is perturbed Schwarzschild metric of the Einstein theory.

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22

Aktar, Mst Ayrin, and Kamalesh Chandra Roy. "Solar System Effects in Schwarzschild Space Time." IOSR Journal of Mathematics 13, no. 01 (2017): 01–05. http://dx.doi.org/10.9790/5728-1301050105.

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23

WU, ZHONG CHAO. "QUANTUM FIELDS IN SCHWARZSCHILD–DE SITTER SPACE." International Journal of Modern Physics D 07, no. 06 (1998): 887–907. http://dx.doi.org/10.1142/s0218271898000589.

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In the No-Boundary Universe a primordial black hole is created from a constrained gravitational instanton. The black hole created is immersed in the de Sitter background with a positive cosmological constant. The constrained instanton is characterized not only by the external parameters, the mass parameter, charge and angular momentum, but also by one more internal parameter, the identification period in the imaginary time coordinate. Although the period has no effect on the black hole background, its inverse is the temperature of the no-boundary state of the perturbation modes perceived by an observer. By using the Bogoliubov transformation, we show that the perturbation modes of both scalar and spinor fields are in thermal equilibrium with the black hole background at the arbitrary temperature. However, for the two extreme cases, the de Sitter and the Nariai models, the no-boundary state remains pure.

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24

Wang, Tian-Yu, and Dong Wang. "Entropic uncertainty relations in Schwarzschild space-time." Physics Letters B 855 (August 2024): 138876. http://dx.doi.org/10.1016/j.physletb.2024.138876.

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25

Guven, Jemal, and Darío Núñez. "Schwarzschild-de Sitter space and its perturbations." Physical Review D 42, no. 8 (1990): 2577–84. http://dx.doi.org/10.1103/physrevd.42.2577.

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26

Felice, F. de, and S. Usseglio-Tomasset. "Schwarzschild spacetime: measurements in orbiting space stations." Classical and Quantum Gravity 10, no. 2 (1993): 353–64. http://dx.doi.org/10.1088/0264-9381/10/2/017.

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27

Bażański, Stanisl/aw L., and Piotr Jaranowski. "Geodesic deviation in the Schwarzschild space‐time." Journal of Mathematical Physics 30, no. 8 (1989): 1794–803. http://dx.doi.org/10.1063/1.528266.

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28

Abbassi, Amir H. "An Extension of Schwarzschild Space tor= 0." Physica Scripta 64, no. 5 (2001): 417–22. http://dx.doi.org/10.1238/physica.regular.064a00417.

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29

Pollock, M. D. "On the Entropy of Schwarzschild Space-Time." Foundations of Physics 43, no. 5 (2013): 615–30. http://dx.doi.org/10.1007/s10701-013-9701-0.

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30

Spaniol, Ednardo Paulo, Ronni Geraldo Gomes Amorim, and Sergio Costa Ulhoa. "On the Hilbert Space in Quantum Gravity." Universe 8, no. 8 (2022): 413. http://dx.doi.org/10.3390/universe8080413.

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This article deals with the fractional problem of Sturm–Liouville and the Hilbert space associated with the solutions of this differential equation. We apply a quantization procedure to Schwarzschild space–time and obtain a fractional differential equation. The Hilbert space for these solutions is established. We used equations arising from quantization for the FRW and Reissner–Nordstron metrics to build the respective Hilbert spaces.

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31

Ulhoa, S. C., A. F. Santos, T. F. Furtado, and F. C. Khanna. "On Hawking entropy revisited." International Journal of Modern Physics A 36, no. 06 (2021): 2150041. http://dx.doi.org/10.1142/s0217751x2150041x.

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The teleparallel gravity, in the weak field approximation, is considered. In the Schwarzschild space–time the gravitational Stefan–Boltzmann law is calculated. Using the first law of thermodynamics, the Hawking entropy and temperature of the black hole are calculated. Thermofield dynamics formalism is used to define the temperature-dependent theory. In addition the gravitational Casimir effect and Stefan–Boltzmann law at zero and finite temperature are calculated in Schwarzschild space–time.

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32

Luo, Cuibai, and Chen Wu. "Dirac quasi-normal frequencies in a noncommutative black hole space–time." Canadian Journal of Physics 97, no. 5 (2019): 562–65. http://dx.doi.org/10.1139/cjp-2018-0174.

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Noncommutative geometry may be an alternative way to quantum gravity. We study the influence of the space–time noncommutative parameter on the Dirac quasi-normal modes in the noncommutative Schwarzschild black hole space–times. In comparison to the commutative Schwarzschild black hole, the numerical results show that the oscillation frequencies and magnitude of the imaginary part of the Dirac quasi-normal modes will increase. However, it is found that the influence of the space–time noncommutative parameter on the Dirac quasi-normal modes is tiny and negligible.

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33

Kuniyal, Ravi Shankar, Rashmi Uniyal, Anindya Biswas, Hemwati Nandan, and K. D. Purohit. "Null geodesics and red–blue shifts of photons emitted from geodesic particles around a noncommutative black hole space–time." International Journal of Modern Physics A 33, no. 16 (2018): 1850098. http://dx.doi.org/10.1142/s0217751x18500987.

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We investigate the geodesic motion of massless test particles in the background of a noncommutative geometry-inspired Schwarzschild black hole. The behavior of effective potential is analyzed in the equatorial plane and the possible motions of massless particles (i.e. photons) for different values of impact parameter are discussed accordingly. We have also calculated the frequency shift of photons in this space–time. Further, the mass parameter of a noncommutative inspired Schwarzschild black hole is computed in terms of the measurable redshift of photons emitted by massive particles moving along circular geodesics in equatorial plane. The strength of gravitational fields of noncommutative geometry-inspired Schwarzschild black hole and usual Schwarzschild black hole in General Relativity is also compared.

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34

CULETU, HRISTU. "IS THE RINDLER HORIZON ENERGY NONVANISHING?" International Journal of Modern Physics D 15, no. 12 (2006): 2177–79. http://dx.doi.org/10.1142/s0218271806009601.

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A nonvanishing value for the Rindler horizon energy is proposed, by an analogy with the "near horizon" Schwarzschild metric. We show that the Rindler horizon energy is given by the same formula E = α/2 obtained by Padmanabhan for the Schwarzschild space–time, where α is the gravitational radius.

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35

Vakili, Babak. "Classical Polymerization of the Schwarzschild Metric." Advances in High Energy Physics 2018 (September 20, 2018): 1–10. http://dx.doi.org/10.1155/2018/3610543.

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We study a spherically symmetric setup consisting of a Schwarzschild metric as the background geometry in the framework of classical polymerization. This process is an extension of the polymeric representation of quantum mechanics in such a way that a transformation maps classical variables to their polymeric counterpart. We show that the usual Schwarzschild metric can be extracted from a Hamiltonian function which in turn gets modifications due to the classical polymerization. Then, the polymer corrected Schwarzschild metric may be obtained by solving the polymer-Hamiltonian equations of motion. It is shown that while the conventional Schwarzschild space-time is a vacuum solution of the Einstein equations, its polymer-corrected version corresponds to an energy-momentum tensor that exhibits the features of dark energy. We also use the resulting metric to investigate some thermodynamical quantities associated with the Schwarzschild black hole, and in comparison with the standard Schwarzschild metric the similarities and differences are discussed.

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36

LUKASH, VLADIMIR N., and VLADIMIR N. STROKOV. "SPACE–TIMES WITH INTEGRABLE SINGULARITY: BLACK–WHITE HOLES AND ASTROGENIC UNIVERSES." International Journal of Modern Physics A 28, no. 02 (2013): 1350007. http://dx.doi.org/10.1142/s0217751x13500073.

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We use the phenomenological approach to study properties of space–time in the vicinity of the Schwarzschild black-hole singularity. Requiring finiteness of the Schwarzschild-like metrics we come to the notion of integrable singularity that is, in a sense, weaker than the conventional singularity and allows the (effective) matter to pass to the white-hole region. This leads to a possibility of generating a new universe there. Thanks to the gravitational field of the singularity, this universe is already born highly inflated ("singularity-induced inflation") before the ordinary inflation starts.

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KONOPKA, TOMASZ. "STATIC ISOTROPIC SPACE–TIMES WITH RADIALLY IMPERFECT FLUIDS." International Journal of Modern Physics D 18, no. 12 (2009): 1821–37. http://dx.doi.org/10.1142/s0218271809015345.

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When one is solving the equations of general relativity in a symmetric sector, it is natural to consider the same symmetry for the geometry and stress–energy. This implies that for static and isotropic space–times, the most general natural stress–energy tensor is a sum of a perfect fluid and a radially imperfect fluid component. In the special situations where the perfect fluid component vanishes or is a space–time constant, the solutions to Einstein's equations can be thought of as modified Schwarzschild and Schwarzschild–de Sitter spaces. Exact solutions of this type are derived and it is shown that whereas deviations from the unmodified solutions can be made small, among the manifestations of the imperfect fluid component is a shift in angular momentum scaling for orbiting test bodies at large radius. Based on this effect, the question of whether the imperfect fluid component can feasibly describe dark matter phenomenology is addressed.

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38

ADAK, M., M. KALAY, and Ö. SERT. "LAGRANGE FORMULATION OF THE SYMMETRIC TELEPARALLEL GRAVITY." International Journal of Modern Physics D 15, no. 05 (2006): 619–34. http://dx.doi.org/10.1142/s0218271806008474.

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We develop a symmetric teleparallel gravity model in a space–time with only the nonmetricity as nonzero, in terms of a Lagrangian quadratic in the nonmetricity tensor. We present a detailed discussion of the variations that may be used for any gravitational formulation. We seek Schwarzschild-type solutions because of its observational significance and obtain a class of solutions that includes Schwarzschild-type, Schwarzschild–de Sitter-type, and Reissner–Nordström-type solutions for certain values of the parameters. We also discuss the physical relevance of these solutions.

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39

CASTRO, C., and J. A. NIETO. "ON (2+2)-DIMENSIONAL SPACE–TIMES, STRINGS AND BLACK HOLES." International Journal of Modern Physics A 22, no. 11 (2007): 2021–45. http://dx.doi.org/10.1142/s0217751x07036191.

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We study black hole-like solutions (space–times with singularities) of Einstein field equations in 3+1 and 2+2 dimensions. We find three different cases associated with hyperbolic homogeneous spaces. In particular, the hyperbolic version of Schwarzschild's solution contains a conical singularity at r = 0 resulting from pinching to zero size r = 0 the throat of the hyperboloid [Formula: see text] and which is quite different from the static spherically symmetric (3+1)-dimensional solution. Static circular symmetric solutions for metrics in 2+2 are found that are singular at ρ = 0 and whose asymptotic ρ→∞ limit leads to a flat (1+2)-dimensional boundary of topology S1 × R2. Finally we discuss the (1+1)-dimensional Bars–Witten stringy black hole solution and show how it can be embedded into our (3+1)-dimensional solutions. Black holes in a (2+2)-dimensional "space–time" from the perspective of complex gravity in 1+1 complex dimensions and their quaternionic and octonionic gravity extensions deserve furher investigation. An appendix is included with the most general Schwarzschild-like solutions in D ≥ 4.

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40

Viennot, David. "Fuzzy Schwarzschild (2 + 1)-spacetime." Journal of Mathematical Physics 63, no. 8 (2022): 082302. http://dx.doi.org/10.1063/5.0091364.

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We present a toy model of a fuzzy Schwarzschild space slice (as a noncommutative manifold), in which quantum mean values and quantum quasi-coherent states (states minimizing the quantum uncertainties) have properties close to the classical slice of ( r, θ) Schwarzschild coordinates (the so-called Flamm’s paraboloid). This fuzzy Schwarzschild slice is built as a deformation of the noncommutative plane. Quantum time observables are introduced to add a time quantization in the model. We study the structure of the quasi-coherent state of the fuzzy Schwarzschild slice with respect to the quasi-coherent state and the deformation states of the noncommutative plane. The quantum dynamics of a fermion interacting with a fuzzy black hole described by the present model is studied. In particular, we study the decoherence effects appearing in the neighborhood of the fuzzy event horizon. An extension of the model to describe a quantum wormhole is also proposed, where we show that fermions cross the wormhole not by traveling by its internal space but by quantum tunneling, in accordance with the non-traversable character of classical Einstein–Rosen bridges.

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41

NOZARI, KOUROSH, and BEHNAZ FAZLPOUR. "THERMODYNAMICS OF NONCOMMUTATIVE SCHWARZSCHILD BLACK HOLE." Modern Physics Letters A 22, no. 38 (2007): 2917–30. http://dx.doi.org/10.1142/s0217732307023602.

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We investigate the effects of space noncommutativity and the generalized uncertainty principle on the thermodynamics of a radiating Schwarzschild black hole. We show that evaporation process is in such a way that black hole reaches a maximum temperature before its final stage of evolution and then cools down to a nonsingular remnant with zero temperature and entropy. We compare our results with more reliable results of string theory. This comparison shows that GUP and space noncommutativity are similar concepts at least from the viewpoint of black hole thermodynamics.

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STUCHLÍK, ZDENĚK, and JIŘÍ KOVÁŘ. "PSEUDO-NEWTONIAN GRAVITATIONAL POTENTIAL FOR SCHWARZSCHILD–DE SITTER SPACE–TIMES." International Journal of Modern Physics D 17, no. 11 (2008): 2089–105. http://dx.doi.org/10.1142/s021827180801373x.

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Pseudo-Newtonian gravitational potential describing the gravitational field of static and spherically symmetric black holes in the universe with a repulsive cosmological constant is introduced. In order to demonstrate the accuracy of the pseudo-Newtonian approach, the related effective potential for test particle motion is constructed and compared with its general-relativistic counterpart given by the Schwarzschild–de Sitter geometry. The results indicate that such an approach could be useful in applications of developed Newtonian theories of accretion disks in astrophysically interesting situations in large galactic structures for the Schwarzschild–de Sitter space–times with the cosmological parameter y = Λ M2/3 ≤ 10-6.

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ESPOSITO, GIAMPIERO, ROBERTO PETTORINO, and PAOLO SCUDELLARO. "ON BOOSTED SPACE-TIMES WITH COSMOLOGICAL CONSTANT AND THEIR ULTRARELATIVISTIC LIMIT." International Journal of Geometric Methods in Modern Physics 04, no. 03 (2007): 361–72. http://dx.doi.org/10.1142/s0219887807002132.

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The problem of deriving a shock-wave geometry with cosmological constant by boosting a Schwarzschild-de Sitter (or anti-de Sitter) black hole is re-examined. Unlike previous works in the literature, we deal with the exact Schwarzschild-de Sitter (or anti-de Sitter) metric. In this exact calculation, where the metric does not depend linearly on the mass parameter, we find a singularity of distributional nature on a null hypersurface, which corresponds to a shock-wave geometry derived in a fully non-perturbative way. The result agrees with previous calculations, where the metric had been linearized in the mass parameter.

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Batista, Márcio, Henrique De Lima, and Wallace Gomes. "Solitons of mean curvature flow in certain warped products: nonexistence, rigidity, and Moser-Bernstein type results." Constructive Mathematical Analysis 8, no. 2 (2025): 117–34. https://doi.org/10.33205/cma.1597851.

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We apply suitable maximum principles to obtain nonexistence and rigidity results for complete mean curvature flow solitons in certain warped product spaces. We also provide applications to self-shrinkers in Euclidean space, as well as to mean curvature flow solitons in real projective, pseudo-hyperbolic, Schwarzschild, and Reissner-Nordstr\"{o}m spaces. Furthermore, we establish new Moser-Bernstein type results for entire graphs constructed over the fiber of the ambient space that are mean curvature flow solitons.

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Kai, Xu, Han-Jie Zhu, Guo-Feng Zhang, Jie-Ci Wang, and Wu-Ming Liu. "Quantum speedup dynamics process in Schwarzschild space–time." Results in Physics 35 (April 2022): 105278. http://dx.doi.org/10.1016/j.rinp.2022.105278.

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Korkina, M. P., and S. V. Buts. "Penrose diagram analysis of Schwarzschild-Friedmann space-time." Soviet Physics Journal 34, no. 7 (1991): 612–16. http://dx.doi.org/10.1007/bf00897991.

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Kawai, T., and E. Sakane. "Distributional Energy-Momentum Densities of Schwarzschild Space-Time." Progress of Theoretical Physics 98, no. 1 (1997): 69–86. http://dx.doi.org/10.1143/ptp.98.69.

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Kawai, T., E. Sakane, and T. Tojo. "Schwarzschild Space-Time in Gauge Theories of Gravity." Progress of Theoretical Physics 99, no. 6 (1998): 971–92. http://dx.doi.org/10.1143/ptp.99.971.

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Vyas, Mukesh K., and Indranil Chattopadhyay. "Radiatively driven relativistic jets in Schwarzschild space-time." Astronomy & Astrophysics 614 (June 2018): A51. http://dx.doi.org/10.1051/0004-6361/201731830.

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Context. Aims. We carry out a general relativistic study of radiatively driven conical fluid jets around non-rotating black holes and investigate the effects and significance of radiative acceleration, as well as radiation drag. Methods. We apply relativistic equations of motion in curved space-time around a Schwarzschild black hole for axis-symmetric one-dimensional jet in steady state, plying through the radiation field of the accretion disc. Radiative moments are computed using information of curved space-time. Slopes of physical variables at the sonic points are found using L’Hôpital’s rule and employing Runge-Kutta’s fourth order method to solve equations of motion. The analysis is carried out using the relativistic equation of state of the jet fluid. Results. The terminal speed of the jet depends on how much thermal energy is converted into jet momentum and how much radiation momentum is deposited onto the jet. Many classes of jet solutions with single sonic points, multiple sonic points, as well as those having radiation driven internal shocks are obtained. Variation of all flow variables along the jet-axis has been studied. Highly energetic electron-proton jets can be accelerated by intense radiation to terminal Lorentz factors γT ~ 3. Moderate terminal speed vT ~ 0.5 is obtained for moderately luminous discs. Lepton dominated jets may achieve γT ~ 10. Conclusions. Thermal driving of the jet itself and radiation driving by accretion disc photons produce a wide-ranging jet solutions starting from moderately strong jets to the relativistic ones. Interplay of intensity, the nature of the radiation field, and the energetics of the jet result in a variety of jet solutions. We show that radiation field is able to induce steady shocks in jets, one of the criteria to explain high-energy power-law emission observed in spectra of some of the astrophysical objects.

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Ulhoa, S. C., and R. G. G. Amorim. "On Teleparallel Quantum Gravity in Schwarzschild Space-Time." Advances in High Energy Physics 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/812691.

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We present the quantization process for Schwarzschild space-time in the context of Teleparallel gravity. In order to achieve such a goal we use the Weyl formalism that establishes a well-defined correspondence between classical quantities which are realized by functions and quantum ones which are realized by operators. In the process of quantization we introduce a fundamental constant that is used to construct what we call the quantum of matter by the imposition of periodic conditions over the eigenfunction.

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