Self-consistent approximate solutions of the semiclassical Einstein equations for a Schwarzschild black hole with its Hawking evaporation

2000 ◽  
Vol 62 (2) ◽  
Author(s):  
Chao-Guang Huang
Keyword(s):  
Black Hole ◽  
Approximate Solutions ◽  
Einstein Equations ◽  
Schwarzschild Black Hole ◽  
Self Consistent ◽  
Hawking Evaporation

DE SITTER-SCHWARZSCHILD BLACK HOLE: ITS PARTICLELIKE CORE AND THERMODYNAMICAL PROPERTIES

1996 ◽  
Vol 05 (05) ◽  
pp. 529-540 ◽  
Author(s):  
I.G. DYMNIKOVA
Keyword(s):  
Black Hole ◽  
Lower Limit ◽  
Mass Parameter ◽  
Hawking Temperature ◽  
Einstein Equations ◽  
Black Hole Mass ◽  
De Sitter ◽  
Schwarzschild Black Hole ◽  
Schwarzschild Solution ◽  
Second Order Phase Transition

We analyze the globally regular solution of the Einstein equations describing a black hole whose singularity is replaced by the de Sitter core. The de Sitter—Schwarzschild black hole (SSBH) has two horizons. Inside of it there exists a particlelike structure hidden under the external horizon. The critical value of mass parameter M cr1 exists corresponding to the degenerate horizon. It represents the lower limit for a black-hole mass. Below M cr1 there is no black hole, and the de Sitter-Schwarzschild solution describes a recovered particlelike structure. We calculate the Hawking temperature of SSBH and show that specific heat is broken and changes its sign at the value of mass M cr 2>M cr 1 which means that a second-order phase transition occurs at that point. We show that the Hawking temperature drops to zero when a mass approaches the lower limit M cr1 .

scholarly journals Self-Consistent Orbital Evolution of a Particle around a Schwarzschild Black Hole

2012 ◽  
Vol 108 (19) ◽  
Author(s):  
Peter Diener ◽  
Ian Vega ◽  
Barry Wardell ◽  
Steven Detweiler
Keyword(s):  
Black Hole ◽  
Orbital Evolution ◽  
Schwarzschild Black Hole ◽  
Self Consistent

Electromagnetic and gravitational signatures of accretion into black holes

2015 ◽  
Vol 24 (09) ◽  
pp. 1542004
Author(s):  
Juan Carlos Degollado
Keyword(s):  
Black Hole ◽  
Maxwell Equations ◽  
Einstein Equations ◽  
System Of Differential Equations ◽  
Charged Fluids ◽  
Schwarzschild Black Hole ◽  
Initial Value ◽  
Stationary Black Hole ◽  
Electromagnetic Signals ◽  
Set Up

In this paper, the gravitational and electromagnetic signals due to accretion of charged fluids into a Schwarzschild black hole is revisited. We set up the perturbed Einstein equations and Maxwell equations coupled to the fluid equations on a stationary black hole as a system of differential equations that can be integrated as an initial value problem. We numerically investigate cases in which we varied the properties of the fluid. Our scenario may provide an electromagnetic counterpart to gravitational waves in many situations of interest, enabling easier extraction and verification of gravitational waveforms from gravitational wave detection. We find that the features of the resulting electromagnetic signals depend on the properties and dynamics of the flow.

scholarly journals Effect of gravitational wave on shadow of a Schwarzschild black hole

2021 ◽  
Vol 81 (6) ◽  
Author(s):  
Mingzhi Wang ◽  
Songbai Chen ◽  
Jiliang Jing
Keyword(s):  
Black Hole ◽  
Gravitational Wave ◽  
Legendre Polynomial ◽  
Vertical Direction ◽  
Einstein Equations ◽  
Schwarzschild Black Hole ◽  
Fractal Structures ◽  
Odd Order ◽  
Particular Solution ◽  
Self Similar

AbstractWe have studied the shadows of a Schwarzschild black hole under a special polar gravitational perturbation, which is a particular solution of Einstein equations expanded up to first order. It is shown that the black hole shadow changes periodically with time and the change of shadow depends on the Legendre polynomial order parameter l and the frequency $$\sigma $$ σ of gravitational wave. For the odd order of Legendre polynomial, the center of shadow oscillates along the direction which is vertical to equatorial plane. For even l, the center of shadow does not move, but the shadow alternately stretches and squeezes with time along the vertical direction. Moreover, the presence of the gravitational wave leads to the self-similar fractal structures appearing in the boundary of the black hole shadow. We also find that this special gravitational wave has a greater influence on the vertical direction of black hole shadow.

scholarly journals CLASSICAL ANALOG OF THE QUANTUM SCHWARZSCHILD BLACK HOLE: LOCAL VS GLOBAL, AND THE MYSTERY OF log 3

2011 ◽  
Vol 26 (01) ◽  
pp. 161-178
Author(s):  
VICTOR BEREZIN
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Event Horizon ◽  
Einstein Equations ◽  
Schwarzschild Black Hole ◽  
Quantum Black Hole ◽  
Classical Analog ◽  
Global Properties

A model is built in which the main global properties of classical and quasiclassical black holes become local. These are the event horizon, "no hair," temperature and entropy. The construction is based on the features of a quantum collapse, discovered when studying some quantum black hole models. But the model is purely classical, and this allows one to use self-consistently the Einstein equations and classical (local) thermodynamics and explain in this way the " log 3" puzzle.

scholarly journals Horizon shells: Classical structure at the horizon of a black hole

2016 ◽  
Vol 25 (12) ◽  
pp. 1644010 ◽  
Author(s):  
Matthias Blau ◽  
Martin O’Loughlin
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Infinite Number ◽  
Mass Formula ◽  
Black Hole Physics ◽  
Einstein Equations ◽  
Schwarzschild Black Hole ◽  
Schwarzschild Solution ◽  
Classical Structure ◽  
Codimension One

We address the question of the uniqueness of the Schwarzschild black hole by considering the following question: How many meaningful solutions of the Einstein equations exist that agree with the Schwarzschild solution (with a fixed mass [Formula: see text]) everywhere except maybe on a codimension one hypersurface? The perhaps surprising answer is that the solution is unique (and uniquely the Schwarzschild solution everywhere in spacetime) unless the hypersurface is the event horizon of the Schwarzschild black hole, in which case there are actually an infinite number of distinct solutions. We explain this result and comment on some of the possible implications for black hole physics.

scholarly journals Phenomenological description of the interior of the Schwarzschild black hole

2015 ◽  
Vol 30 (15) ◽  
pp. 1550091 ◽  
Author(s):  
Hikaru Kawai ◽  
Yuki Yokokura
Keyword(s):  
Black Hole ◽  
Hawking Radiation ◽  
Weyl Tensor ◽  
Radial Direction ◽  
Heat Bath ◽  
Radiation Energy ◽  
The Other ◽  
Schwarzschild Black Hole ◽  
Self Consistent ◽  
Consistent Solution

We discuss a sufficiently large four-dimensional Schwarzschild black hole which is in equilibrium with a heat bath. In other words, we consider a black hole which has grown up from a small one in the heat bath adiabatically. We express the metric of the interior of the black hole in terms of two functions: One is the intensity of the Hawking radiation, and the other is the ratio between the radiation energy and the pressure in the radial direction. Especially in the case of conformal matters we check that it is a self-consistent solution of the semiclassical Einstein equation, Gμν = 8πG〈Tμν〉. It is shown that the strength of the Hawking radiation is proportional to the c-coefficient, that is, the coefficient of the square of the Weyl tensor in the four-dimensional Weyl anomaly.

The Schwarzschild black hole

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Black Hole ◽  
Gravitational Field ◽  
Equilibrium Configuration ◽  
Original Form ◽  
Schwarzschild Black Hole ◽  
Schwarzschild Metric ◽  
Schwarzschild Geometry

This chapter discusses the Schwarzschild black hole. It demonstrates how, by a judicious change of coordinates, it is possible to eliminate the singularity of the Schwarzschild metric and reveal a spacetime that is much larger, like that of a black hole. At the end of its thermonuclear evolution, a star collapses and, if it is sufficiently massive, does not become stabilized in a new equilibrium configuration. The Schwarzschild geometry must therefore represent the gravitational field of such an object up to r = 0. This being said, the Schwarzschild metric in its original form is singular, not only at r = 0 where the curvature diverges, but also at r = 2m, a surface which is crossed by geodesics.

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