The lower sensitivities and the sensitivities of the Schwarzschild metric near the Schwarzschild black hole

2021 ◽  
Author(s):  
Mohammadreza Molaei
Keyword(s):  
Black Hole ◽  
Schwarzschild Black Hole ◽  
Schwarzschild Metric

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.

scholarly journals The geodesics structure of Schwarzschild black hole immersed in an electromagnetic universe

2017 ◽  
Vol 26 (14) ◽  
pp. 1750169 ◽  
Author(s):  
A. Al-Badawi ◽  
M. Q. Owaidat ◽  
S. Tarawneh
Keyword(s):  
Black Hole ◽  
Analytical Solution ◽  
Exact Analytical Solution ◽  
Proper Time ◽  
Massive Particle ◽  
Schwarzschild Black Hole ◽  
Circular Orbits ◽  
Schwarzschild Metric ◽  
Effective Potentials ◽  
Em Field

The geodesic equations are considered in a spacetime that represents a Schwarzschild metric coupled to a uniform external electromagnetic (em) field. Due to the em field horizon shrinks and geodesics are modified. By analyzing the behavior of the effective potentials for the massless and massive particle we study the radial and circular trajectories. Radial geodesics for both photons and particles are solved exactly. It is shown that a particle that falls toward the horizon in a finite proper time slows down so that the particle reaches the singularity slower than Schwarzschild case. Timelike and null circular geodesics are investigated. We have shown that, there are no stable circular orbits for photons, however stable and unstable second-kind orbits exist for the massive particle. An exact analytical solution for the innermost stable circular orbits (ISCO) has been obtained. It has been shown that the radius of the ISCO shrinks due to the presence of the em field.

On the equations governing the perturbations of the Schwarzschild black hole

1975 ◽  
Vol 343 (1634) ◽  
pp. 289-298 ◽  
Keyword(s):  
Black Hole ◽  
Schrödinger Equation ◽  
Time Dependence ◽  
Spherical Harmonics ◽  
Schrodinger Equation ◽  
Schwarzschild Black Hole ◽  
Schwarzschild Metric ◽  
One Dimensional ◽  
The Subject

A coherent self-contained account of the equations governing the perturbations of the Schwarzschild black hole is given. In particular, the relations between the equations of Bardeen & Press, of Zerilli and of Regge & Wheeler are explicitly established. The equations governing the perturbations of the vacuum Schwarzschild metric - the Schwarzschild black hole-have been the subject of many investigations (Regge & Wheeler 1957; Vishveshwara 1970; Edelstein & Vishveshwara 1970; Zerilli 1970 a, b ; Fackerell 1971; Bardeen & Press 1972; Friedman 1973). Nevertheless, there continues to be some elements of mystery shrouding the subject. Thus, Zerilli (1970a) showed that the equations governing the perturbation, properly analysed into spherical harmonics (belonging to the different l values) and with a time dependence iot , can be reduced to a one dimensional Schrodinger equation of the form

scholarly journals Hawking radiation in κ-spacetime

2017 ◽  
Vol 32 (13) ◽  
pp. 1750072 ◽  
Author(s):  
E. Harikumar ◽  
N. S. Zuhair
Keyword(s):  
Black Hole ◽  
Hawking Radiation ◽  
Gordon Equation ◽  
Symmetric Tensor ◽  
Hawking Temperature ◽  
Momentum Dependence ◽  
Conformally Flat ◽  
Schwarzschild Black Hole ◽  
Schwarzschild Metric ◽  
Klein Gordon

In this paper, we analyze the Hawking radiation of a [Formula: see text]-deformed-Schwarzschild black hole and obtain the deformed Hawking temperature. For this, we first derive deformed metric for the [Formula: see text]-spacetime, which in the generic case, is not a symmetric tensor and also has a momentum dependence. We show that the Schwarzschild metric obtained in the [Formula: see text]-deformed spacetime has a dependence on energy. We use the fact that the deformed metric is conformally flat in the 1[Formula: see text]+[Formula: see text]1 dimensions to solve the [Formula: see text]-deformed Klein–Gordon equation in the background of the Schwarzschild metric. The method of Bogoliubov coefficients is then used to calculate the thermal spectrum of [Formula: see text]-deformed-Schwarzschild black hole and show that the Hawking temperature is modified by the noncommutativity of the [Formula: see text]-spacetime.

What is the meaning of the pullback Schwarzschild metric?

2019 ◽  
Author(s):  
Matheus Pereira Lobo
Keyword(s):  
Black Hole ◽  
Thought Experiment ◽  
Schwarzschild Metric

We propose a thought experiment regarding the pullback Schwarzschild metric, considering that there is no interior of a black hole.

scholarly journals Black hole S-matrix for a scalar field

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Panos Betzios ◽  
Nava Gaddam ◽  
Olga Papadoulaki
Keyword(s):  
Black Hole ◽  
Normal Modes ◽  
Massless Scalar ◽  
Scattering Process ◽  
Schwarzschild Black Hole ◽  
Asymptotically Flat ◽  
Scalar Particles ◽  
Black Hole Background ◽  
S Matrix ◽  
Do So

Abstract We describe a unitary scattering process, as observed from spatial infinity, of massless scalar particles on an asymptotically flat Schwarzschild black hole background. In order to do so, we split the problem in two different regimes governing the dynamics of the scattering process. The first describes the evolution of the modes in the region away from the horizon and can be analysed in terms of the effective Regge-Wheeler potential. In the near horizon region, where the Regge-Wheeler potential becomes insignificant, the WKB geometric optics approximation of Hawking’s is replaced by the near-horizon gravitational scattering matrix that captures non-perturbative soft graviton exchanges near the horizon. We perform an appropriate matching for the scattering solutions of these two dynamical problems and compute the resulting Bogoliubov relations, that combines both dynamics. This allows us to formulate an S-matrix for the scattering process that is manifestly unitary. We discuss the analogue of the (quasi)-normal modes in this setup and the emergence of gravitational echoes that follow an original burst of radiation as the excited black hole relaxes to equilibrium.

scholarly journals Null Geodesics and Strong Field Gravitational Lensing in a String Cloud Background

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
M. Sharif ◽  
Sehrish Iftikhar
Keyword(s):  
Black Hole ◽  
Gravitational Lensing ◽  
Galactic Center ◽  
Deflection Angle ◽  
Orbital Motion ◽  
Strong Field ◽  
Schwarzschild Black Hole ◽  
Field Limit ◽  
Null Geodesics ◽  
Supermassive Black Hole

This paper is devoted to studying two interesting issues of a black hole with string cloud background. Firstly, we investigate null geodesics and find unstable orbital motion of particles. Secondly, we calculate deflection angle in strong field limit. We then find positions, magnifications, and observables of relativistic images for supermassive black hole at the galactic center. We conclude that string parameter highly affects the lensing process and results turn out to be quite different from the Schwarzschild black hole.

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