ON THE WHEELER-DEWITT EQUATION FOR BLACK HOLES

1994 ◽  
Vol 03 (03) ◽  
pp. 579-591 ◽  
Author(s):  
M.D. POLLOCK
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Apparent Horizon ◽  
Hamiltonian Formalism ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Two Dimensional ◽  
Superstring Theory

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.

scholarly journals On-axis scalar absorption cross section of Kerr–Newman black holes: Geodesic analysis, sinc and low-frequency approximations

2018 ◽  
Vol 27 (11) ◽  
pp. 1843012 ◽  
Author(s):  
Carolina L. Benone ◽  
Luiz C. S. Leite ◽  
Luís C. B. Crispino ◽  
Sam R. Dolan
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Cross Section ◽  
Absorption Cross Section ◽  
Rotation Axis ◽  
Low Frequency ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Absorption Cross ◽  
Newman Black Hole

We investigate null geodesics impinging parallel to the rotation axis of a Kerr–Newman black hole, and show that the absorption cross section for a massless scalar field in the eikonal limit can be described in terms of the photon orbit parameters. We compare our sinc and low-frequency approximations with numerical results, showing that they are in excellent agreement.

scholarly journals Gravitational collapse in the AdS background and the black hole formation

2016 ◽  
Vol 25 (01) ◽  
pp. 1650005 ◽  
Author(s):  
Alireza Allahyari ◽  
Javad T. Firouzjaee ◽  
Reza Mansouri
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Event Horizon ◽  
Gravitational Collapse ◽  
Apparent Horizon ◽  
Rapid Change ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Hole Formation ◽  
Thermalization Time

We study the time evolution of the Misner-Sharp mass and the apparent horizon for gravitational collapse of a massless scalar field in the [Formula: see text] spacetime for both cases of narrow and broad waves by numerically solving the Einstein’s equations coupled to a massless scalar field. This is done by relying on the full dynamics of the collapse including the concept of the dynamical horizon. It turns out that the Misner-Sharp mass is everywhere constant except for a rapid change across a thin shell defined by the density profile of the collapsing wave. By studying the evolution of the apparent horizon, indicating the formation of a black hole at different times we see how asymptotically an event horizon forms. The dependence of the thermalization time on the radius of the initial black hole event horizon is also studied.

scholarly journals DISCUSSION ON SOME CHARACTERISTICS OF CHARGED BRANE-WORLD BLACK HOLES

2009 ◽  
Vol 24 (04) ◽  
pp. 719-739 ◽  
Author(s):  
M. KALAM ◽  
F. RAHAMAN ◽  
A. GHOSH ◽  
B. RAYCHAUDHURI
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Gravitational Field ◽  
Scalar Field ◽  
Brane World ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Effective Potentials ◽  
Test Particles ◽  
Jacobi Formalism

Several physical natures of charged brane-world black holes are investigated. Firstly, the timelike and null geodesics of the charged brane-world black holes are presented. We also analyze all the possible motions by plotting the effective potentials for various parameters for circular and radial geodesics. Secondly, we investigate the motion of test particles in the gravitational field of the charged brane-world black holes using the Hamilton–Jacobi formalism. We consider charged and uncharged test particles and examine their behavior in both static and nonstatic cases. Thirdly, the thermodynamics of the charged brane-world black holes are studied. Finally, it is shown that there is no phenomenon of superradiance for an incident massless scalar field for such a black hole.

scholarly journals Analytic treatment of near-extremal charged black holes supporting non-minimally coupled massless scalar clouds

2020 ◽  
Vol 80 (12) ◽  
Author(s):  
Shahar Hod
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Coupling Parameter ◽  
Analytical Formula ◽  
Scalar Fields ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Charged Black Holes ◽  
Black Hole Spacetimes ◽  
Electromagnetic Tensor

AbstractIt has recently been revealed that massless scalar fields which are non-minimally coupled to the Maxwell electromagnetic tensor can be supported in the exterior spacetime regions of spherically symmetric charged black holes. The boundary between scalarized charged black-hole spacetimes and bald (scalarless) Reissner–Nordström black holes is determined by the presence of a critical existence-line which describes spatially regular linearized scalar ‘clouds’ that are supported in the black-hole spacetime. In the present paper we use analytical techniques in order to solve the Klein–Gordon wave equation for the non-minimally coupled linearized scalar fields in the spacetimes of near-extremal supporting black holes. In particular, we derive a remarkably compact analytical formula for the discrete resonant spectrum $$\{\alpha (l,Q/M;n)\}^{n=\infty }_{n=1}$$ { α ( l , Q / M ; n ) } n = 1 n = ∞ which characterizes the dimensionless coupling parameter of the composed Reissner–Nordström-black-hole-nonminimally-coupled-massless-scalar-field configurations along the critical existence-line of the Einstein–Maxwell-scalar theory (here Q/M is the dimensionless charge-to-mass ratio of the central supporting black hole and l is the angular harmonic index of the supported scalar configurations).

Hawking radiation of analogous acoustic black holes

2020 ◽  
Vol 35 (28) ◽  
pp. 2050236
Author(s):  
Shiwei Zhou ◽  
Kui Xiao
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Hawking Radiation ◽  
Emission Rate ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Spherically Symmetric ◽  
Sound Waves ◽  
Flowing Fluid ◽  
Acoustic Black Holes

Propagation of sound waves in a flowing fluid can be viewed as a minimally coupled massless scalar field propagating in curved spacetime. The analogue Hawking radiation from a spherically symmetric acoustic black hole and a (2 + 1)-dimensional rotating acoustic black hole are investigated respectively in Damour–Ruffini’s method. The emission rate and Hawking temperature are obtained, which are related to acoustic black holes parameter.

ON THE QUANTIZATION OF CHARGED BLACK HOLES

1998 ◽  
Vol 07 (04) ◽  
pp. 521-534 ◽  
Author(s):  
M. D. POLLOCK
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Apparent Horizon ◽  
Hamiltonian Formalism ◽  
Back Reaction ◽  
Cauchy Horizon ◽  
Electron Positron ◽  
Extremal Limit ◽  
Electron Positron Pair ◽  
Constant Charge

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.

scholarly journals Scattering of massless scalar field by charged dilatonic black holes

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
Yang Huang ◽  
Hongsheng Zhang
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Scalar Field ◽  
Cross Sections ◽  
Wave Theory ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Scattering Cross ◽  
Hole Charge ◽  
Scattering Cross Sections

Abstract Wave propagations in the presence of black holes is a significant problem both in theoretical and observational aspects, especially after the discovery of gravitational wave and confirmation of black holes. We study the scattering of massless scalar field by a charged dilatonic black hole in frame of full wave theory. We apply partial wave method to obtain the scattering cross sections of the scalar field, and investigate how the black hole charge affects the scalar scattering cross sections. Furthermore, we investigate the Regge pole approach of the scattering cross section of the dilatonic black hole. We find that in order to obtain results at the same precision, we need more Regge poles as the black hole charge increases. We compare the results in the full wave theory and results in the classical geodesic scattering and the semi-classical glory approximations, and demonstrate the improvements and power of our approach.

scholarly journals On black hole structures in scalar–tensor theories of gravity

2016 ◽  
Vol 25 (09) ◽  
pp. 1641005 ◽  
Author(s):  
Kirill A. Bronnikov ◽  
Júlio C. Fabris ◽  
Denis C. Rodrigues
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Scalar Field ◽  
Metric Regularity ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Singular Behavior ◽  
Nonminimal Coupling ◽  
Theories Of Gravity ◽  
Scalar Gravity

We review some properties of black hole structures appearing in gravity with a massless scalar field, with both minimal and nonminimal coupling. The main properties of the resulting cold black holes are described. The study of black holes in scalar-gravity systems is extended to [Formula: see text]-essence theories, and some examples are explicitly worked out. In these cases, even while the existence of horizons is possible, the metric regularity requirement on the horizon implies either a cold black type structure or a singular behavior of the scalar field.

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