scholarly journals DE BROGLIE–BOHM INTERPRETATION FOR WAVE FUNCTION OF REISSNER–NORDSTRÖM–DE SITTER BLACK HOLE

2000 ◽  
Vol 15 (14) ◽  
pp. 2059-2075 ◽  
Author(s):  
MASAKATSU KENMOKU ◽  
HIROTO KUBOTANI ◽  
EIICHI TAKASUGI ◽  
YUKI YAMAZAKI
Keyword(s):  
Black Hole ◽  
Wave Function ◽  
Spherically Symmetric ◽  
De Sitter ◽  
Semiclassical Gravity ◽  
Symmetric Geometry ◽  
Bohm Interpretation ◽  
Canonical Quantum ◽  
Ordinary Quantum ◽  
De Broglie Bohm

We study the canonical quantum theory of the spherically symmetric geometry with the cosmological constant and the electromagnetic field. We obtain a solution of the Wheeler–DeWitt equation for the geometrical variables and investigate the wave function from a viewpoint of the de Broglie–Bohm interpretation of the ordinary quantum mechanics. The de Broglie–Bohm interpretation introduces deterministic rigid trajectories on the minisuperspace without any outside observers nor the collapse of the wave function. It is shown that the wave function does not only correspond to the classical Reissner–Nordström–de Sitter black hole in the semiclassical region, but it also represents quantum geometrical fluctuations near the black hole horizon and the cosmological one. The result suggests that the semiclassical gravity on which the Hawking radiation is based is broken near the horizons.

scholarly journals LUKEWARM BLACK HOLES IN QUADRATIC GRAVITY

2011 ◽  
Vol 26 (14) ◽  
pp. 999-1007 ◽  
Author(s):  
JERZY MATYJASEK ◽  
KATARZYNA ZWIERZCHOWSKA
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Event Horizon ◽  
Fourth Order ◽  
Spherically Symmetric ◽  
Cosmological Horizon ◽  
De Sitter ◽  
Quadratic Gravity ◽  
De Sitter Universe ◽  
Electrically Charged

Perturbative solutions to the fourth-order gravity describing spherically-symmetric, static and electrically charged black hole in an asymptotically de Sitter universe is constructed and discussed. Special emphasis is put on the lukewarm configurations, in which the temperature of the event horizon equals the temperature of the cosmological horizon.

scholarly journals REGULAR BLACK HOLES IN AN ASYMPTOTICALLY DE SITTER UNIVERSE

2008 ◽  
Vol 23 (40) ◽  
pp. 3377-3392 ◽  
Author(s):  
JERZY MATYJASEK ◽  
DARIUSZ TRYNIECKI ◽  
MARIUSZ KLIMEK
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Nonlinear Electrodynamics ◽  
Spherically Symmetric ◽  
De Sitter ◽  
Coupled Equations ◽  
Sitter Universe ◽  
De Sitter Universe ◽  
Horizon Geometry ◽  
Interesting Solution

A regular solution of the system of coupled equations of the nonlinear electrodynamics and gravity describing static and spherically-symmetric black holes in an asymptotically de Sitter universe is constructed and analyzed. Special emphasis is put on the degenerate configurations (when at least two horizons coincide) and their near horizon geometry. It is explicitly demonstrated that approximating the metric potentials in the region between the horizons by simple functions and making use of a limiting procedure one obtains the solutions constructed from maximally symmetric subspaces with different absolute values of radii. Topologically they are AdS2×S2 for the cold black hole, dS2×S2 when the event and cosmological horizon coincide, and the Plebański–Hacyan solution for the ultraextremal black hole. A physically interesting solution describing the lukewarm black holes is briefly analyzed.

EXACT SOLUTIONS OF DILATON GRAVITY WITH (ANTI)-DE SITTER ASYMPTOTICS

2014 ◽  
Vol 29 (02) ◽  
pp. 1450010 ◽  
Author(s):  
S. MIGNEMI
Keyword(s):  
Black Hole ◽  
Exact Solutions ◽  
Maxwell Field ◽  
Spherically Symmetric ◽  
Dilaton Gravity ◽  
De Sitter ◽  
Asymptotically Flat ◽  
Black Hole Solutions

We present a technique for obtaining exact spherically symmetric asymptotically de Sitter (dS) or anti-de Sitter (adS) black hole solutions of dilaton gravity with generic coupling to Maxwell field, starting from asymptotically flat solutions and adding a suitable dilaton potential to the action.

Further spherically symmetric solutions

2021 ◽  
pp. 249-259
Author(s):  
Andrew M. Steane
Keyword(s):  
Black Hole ◽  
Field Equation ◽  
Cosmological Constant ◽  
Electromagnetic Fields ◽  
Stellar Structure ◽  
Spherically Symmetric ◽  
De Sitter ◽  
Schwarzschild Solution ◽  
Spherically Symmetric Solutions ◽  
Structure Equations

We obtain the interior Schwarzschild solution; the stellar structure equations (Tolman-Oppenheimer-Volkoff); the Reissner-Nordstrom metric (charged black hole) and the de Sitter-Schwarzschild metric. These both illustrate how the field equation is tackled in non-vacuum cases, and bring out some of the physics of stars, electromagnetic fields and the cosmological constant.

The spatially flat Friedmann equation for early rainbow universe

2015 ◽  
Vol 30 (31) ◽  
pp. 1550165
Author(s):  
Han Siong Ch’ng ◽  
Geri Gopir ◽  
Shahidan Radiman
Keyword(s):  
Early Universe ◽  
Quantum Cosmology ◽  
Gravitational Constant ◽  
Friedmann Equation ◽  
Late Time ◽  
Friedmann Equations ◽  
Bohm Interpretation ◽  
The One ◽  
Canonical Quantum ◽  
De Broglie Bohm

We derive the spatially flat rainbow-Friedmann equation from de Broglie–Bohm interpretation in canonical quantum cosmology. Our result shows that the spatially flat rainbow-Friedmann equations of early and late-time universe are having different forms. The spatially flat rainbow-Friedmann equation of early universe which is obtained in this paper is quite different from the one which was initially derived by Magueijo and Smolin [Class. Quantum Grav. 21, 1725 (2004)]. However, the spatially flat rainbow-Friedmann equation for late-time universe obtained in this paper is found to be the same as the one derived by Magueijo and Smolin (for the case [Formula: see text] and Newton’s gravitational constant [Formula: see text]. The new spatially flat rainbow-Friedmann equation obtained in this paper could provide an alternative way in understanding the evolution of the early rainbow universe.

scholarly journals THERMODYNAMICS OF HORIZONS: A COMPARISON OF SCHWARZSCHILD, RINDLER AND de SITTER SPACETIMES

2002 ◽  
Vol 17 (15n17) ◽  
pp. 923-942 ◽  
Author(s):  
T. PADMANABHAN
Keyword(s):  
Black Hole ◽  
Vacuum State ◽  
Quantum States ◽  
Spherically Symmetric ◽  
De Sitter ◽  
Schwarzschild Black Hole ◽  
Black Hole Spacetimes ◽  
Conformal Field ◽  
Symmetric Spacetimes ◽  
Transverse Area

The notions of temperature, entropy and 'evaporation', usually associated with spacetimes with horizons, are analyzed using general approach and the following results, applicable to different spacetimes, are obtained at one go. (i) The concept of temperature associated with the horizon is derived in a unified manner and is shown to arise from purely kinematic considerations. (ii) QFT near any horizon is mapped to a conformal field theory without introducing concepts from string theory. (iii) For spherically symmetric spacetimes (in D = 1 + 3) with a horizon at r = l, the partition function has the generic form Z ∝ exp [S - βE], where S = (1/4)4πl2 and |E| = (l/2). This analysis reproduces the conventional result for the black hole spacetimes and provides a simple and consistent interpretation of entropy and energy E = - (1/2)H-1 for deSitter spacetime. The classical Einstein's equations for this spacetime can be expressed as a thermodynamic identity, TdS - dE = PdV with the same variables. (iv) For the Rindler spacetime the entropy per unit transverse area turns out to be (1/4) while the energy is zero. (v) In the case of a Schwarzschild black hole there exist quantum states (like Unruh vacuum) which are not invariant under time reversal and can describe black hole evaporation. There also exist quantum states (like Hartle-Hawking vacuum) in which temperature is well-defined but there is no flow of radiation to infinity. In the case of deSitter universe or Rindler patch in flat spacetime, one usually uses quantum states analogous to Hartle-Hawking vacuum and obtains a temperature without the corresponding notion of evaporation. It is, however, possible to construct the analogues of Unruh vacuum state in the other cases as well. The implications are briefly discussed.

scholarly journals Quantum and Classical Cosmology in the Brans–Dicke Theory

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 286
Author(s):  
Carla R. Almeida ◽  
Olesya Galkina ◽  
Julio César Fabris
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Classical Model ◽  
Bohmian Mechanics ◽  
Finite Energy ◽  
Energy Conditions ◽  
Interpretation Of Quantum Mechanics ◽  
Expectation Values ◽  
Bohm Interpretation ◽  
De Broglie Bohm

In this paper, we discuss classical and quantum aspects of cosmological models in the Brans–Dicke theory. First, we review cosmological bounce solutions in the Brans–Dicke theory that obeys energy conditions (without ghost) for a universe filled with radiative fluid. Then, we quantize this classical model in a canonical way, establishing the corresponding Wheeler–DeWitt equation in the minisuperspace, and analyze the quantum solutions. When the energy conditions are violated, corresponding to the case ω<−32, the energy is bounded from below and singularity-free solutions are found. However, in the case ω>−32, we cannot compute the evolution of the scale factor by evaluating the expectation values because the wave function is not finite (energy spectrum is not bounded from below). However, we can analyze this case using Bohmian mechanics and the de Broglie–Bohm interpretation of quantum mechanics. Using this approach, the classical and quantum results can be compared for any value of ω.

GRAVITATIONAL THERMODYNAMICS AND THE WHEELER–DEWITT EQUATION

2011 ◽  
Vol 20 (01) ◽  
pp. 23-42 ◽  
Author(s):  
M. D. POLLOCK
Keyword(s):  
Black Hole ◽  
Wave Function ◽  
Boundary Conditions ◽  
Cosmological Constant ◽  
Apparent Horizon ◽  
De Sitter Space ◽  
Hawking Temperature ◽  
De Sitter ◽  
Schwarzschild Black Hole ◽  
Gravitational Thermodynamics

In a previous paper, we have derived the Hawking temperature T H = 1/8πM for a Schwarzschild black hole of mass M, starting from the Wheeler–DeWitt for the wave function Ψ on the apparent horizon, due to Tomimatsu. Here we discuss the derivation of this result in greater detail, with particular regard to the Euclideanization procedure involved and the boundary conditions on the horizon. Further, analysis of the de Sitter space-time generated by a cosmological constant Λ yields the temperature [Formula: see text] found by Gibbons and Hawking, which thus vindicates the method. The emission of radiation occurs with preservation of unitarity, and hence entropy, which is substantiated by a global thermodynamical argument in the case of the black hole.

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