scholarly journals Scalar Waves in the Exterior of a Schwarzschild Black Hole

1974 ◽  
Vol 64 ◽  
pp. 95-95
Author(s):  
S. Persides
Keyword(s):  
Black Hole ◽  
Wave Equation ◽  
Scalar Field ◽  
Schwarzschild Black Hole ◽  
Radial Wave ◽  
Point Test ◽  
Fourier And Laplace Transforms ◽  
Image Position ◽  
Interior Solutions ◽  
Radial Wave Equation

Fourier and Laplace transforms are used to study rigorously the properties of a test scalar field PS in the exterior of a Schwarzschild black hole of the mass m. In the Fourier analysis we examine the properties of the solutions of the radial wave equation and the relations of the exterior and interior solutions of the following four cases: (i) ω ≠ 0, m≠0, (ii) ω=0, m≠0, (iii) ω≠0, m=0, (iv) ω=0, m=0.In the Laplace analysis we show rigorously the following theorem: If ψ(t, r, τ, ϕ) is the field of a point test particle falling into the black hole, and lim Ψ exists, then lim Ψ = 0. The proof of this theorem is based on the facts that (a)t+2m ln (r − 2m) is finite for the particle even on the horizon, and (b) the behavior of Ψ as t → + ∞ is related to its Laplace transform near the origin of the complex plane.

Entropy in a d-dimensional charged black hole

2018 ◽  
Vol 33 (27) ◽  
pp. 1850159 ◽  
Author(s):  
Shad Ali ◽  
Xin-Yang Wang ◽  
Wen-Biao Liu
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Hawking Radiation ◽  
Space Time ◽  
Charged Black Hole ◽  
Schwarzschild Black Hole ◽  
Proportionality Coefficient ◽  
Proportional Relation ◽  
Hamiltonian Analysis ◽  
Interior Volume

Christodoulou and Rovelli have shown that the interior volume of a Schwarzschild black hole grows linearly with time. The entropy of a scalar field in this interior volume of a Schwarzschild black hole has been calculated and shown to increase linearly with the advanced time too. In this paper, considering Hawking radiation from a d-dimensional charged black hole, we investigate the proportional relation between the entropy of the scalar field in the interior volume and the Bekenstein–Hawking entropy using the method of our previous work. We also derive this proportionality relation using Hamiltonian analysis and find a consistent result. We then investigate the proportionality coefficient with respect to d and find that it gradually decreases as the dimension of space–time increases.

scholarly journals Quasi-normal modes and the area spectrum of a near extremal de Sitter black hole with conformally coupled scalar field

2015 ◽  
Vol 30 (11) ◽  
pp. 1550057 ◽  
Author(s):  
Sharmanthie Fernando
Keyword(s):  
Black Hole ◽  
Wave Equation ◽  
Scalar Field ◽  
Normal Modes ◽  
Type Equation ◽  
Area Spectrum ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
De Sitter ◽  
Quasi Normal Mode

In this paper, we have studied a black hole in de Sitter space which has a conformally coupled scalar field in the background. This black hole is also known as the MTZ black hole. We have obtained exact values for the quasi-normal mode (QNM) frequencies under massless scalar field perturbations. We have demonstrated that when the black hole is near-extremal, that the wave equation for the massless scalar field simplifies to a Schrödinger type equation with the well-known Pöschl–Teller potential. We have also used sixth-order WKB approximation to compute QNM frequencies to compare with exact values obtained via the Pöschl–Teller method for comparison. As an application, we have obtained the area spectrum using modified Hods approach and show that it is equally spaced.

Gravitational synchrotron radiation in the metric of a new theory of gravitation

1980 ◽  
Vol 58 (11) ◽  
pp. 1595-1598 ◽  
Author(s):  
R. B. Mann ◽  
J. W. Moffat
Keyword(s):  
Black Hole ◽  
Wave Equation ◽  
Synchrotron Radiation ◽  
Gravitational Radiation ◽  
Field Structure ◽  
Astrophysical Object ◽  
Schwarzschild Black Hole ◽  
Null Surface ◽  
Strong Source ◽  
Theory Of Gravitation

The wave equation for a scalar field ψ is solved in the background metric of a new theory of gravity, based on a non-Riemannian field structure with a nonsymmetric Hermitian gμν. In contrast to the solution of the problem in a Schwarzschild background metric, in which only orbits close to r ~ 3M yield significant gravitational radiation, the new metric leads to an effective potential with stable orbits for a substantial range of r. The solution yields ψ = (1 − ℓ4/r4)−1/2ψGR where ℓ is a new integration constant. The null surface r = ℓ determines an astrophysical object called a "deflectar", which for ℓ > 2M conceals the Schwarzschild black-hole event horizon at r = 2M. As r → ℓ the gravitational synchrotron radiation increases to infinity. The actual power output of gravitational radiation for physically allowed stable orbits closest to r = ℓ is estimated, demonstrating that a deflectar is a potentially strong source of gravitational radiation.

scholarly journals ENTROPY OF SCALAR FIELD NEAR A SCHWARZSCHILD BLACK HOLE HORIZON

2006 ◽  
Vol 21 (30) ◽  
pp. 6183-6190 ◽  
Author(s):  
M. R. SETARE
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Spherical Shell ◽  
Polarization Effect ◽  
Vacuum Polarization ◽  
Mixed Boundary Condition ◽  
Mixed Boundary ◽  
Massive Scalar ◽  
Schwarzschild Black Hole ◽  
Massive Scalar Field

In this paper we compute the correction to the entropy of Schwarzschild black hole due to the vacuum polarization effect of massive scalar field. The Schwarzschild black hole is supposed to be confined in spherical shell. The scalar field obeying mixed boundary condition on the spherical shell.

scholarly journals Massive scalar field quasinormal modes of a Schwarzschild black hole surrounded by quintessence

Open Physics ◽  
2008 ◽  
Vol 6 (2) ◽  
Author(s):  
Chunrui Ma ◽  
Yuanxing Gui ◽  
Wei Wang ◽  
Fujun Wang
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Quasinormal Modes ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Massive Scalar ◽  
Schwarzschild Black Hole ◽  
Third Order ◽  
Massive Scalar Field ◽  
Absolute Value

AbstractWe present the quasinormal frequencies of the massive scalar field in the background of a Schwarzchild black hole surrounded by quintessence with the third-order WKB method. The mass of the scalar field u plays an important role in studying the quasinormal frequencies, the real part of the frequencies increases linearly as mass of the field u increases, while the imaginary part in absolute value decreases linearly which leads to damping more slowly than the massless scalar field. The frequencies have a limited value, so it is easier to detect the quasinormal modes. Moreover, owing to the presence of the quintessence, the massive scalar field damps more slowly.

scholarly journals Geodesic motion near self-gravitating scalar field configurations

2019 ◽  
Vol 27 (3) ◽  
pp. 231-241
Author(s):  
Ivan M. Potashov ◽  
Julia V. Tchemarina ◽  
Alexander N. Tsirulev
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Circular Orbit ◽  
Naked Singularity ◽  
Schwarzschild Black Hole ◽  
Null Geodesics ◽  
Naked Singularities ◽  
Test Particles ◽  
Stable Circular Orbit ◽  
Innermost Stable Circular Orbit

We study the geodesics motion of neutral test particles in the static spherically symmetric spacetimes of black holes and naked singularities supported by a selfgravitating real scalar field. The scalar field is supposed to model dark matter surrounding some strongly gravitating object such as the centre of our Galaxy. The behaviour of timelike and null geodesics very close to the centre of such a configuration crucially depends on the type of spacetime. It turns out that a scalar field black hole, analogously to a Schwarzschild black hole, has the innermost stable circular orbit and the (unstable) photon sphere, but their radii are always less than the corresponding ones for the Schwarzschild black hole of the same mass; moreover, these radii can be arbitrarily small. In contrast, a scalar field naked singularity has neither the innermost stable circular orbit nor the photon sphere. Instead, such a configuration has a spherical shell of test particles surrounding its origin and remaining in quasistatic equilibrium all the time. We also show that the characteristic properties of null geodesics near the centres of a scalar field naked singularity and a scalar field black hole of the same mass are qualitatively different.

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