Fluctuation around horizon on a Schwarzschild black hole using the null geodesic method

2009 ◽  
Vol 4 (4) ◽  
pp. 530-533
Author(s):  
Ji-li Huang ◽  
Wen-biao Liu
Keyword(s):  
Black Hole ◽  
Null Geodesic ◽  
Schwarzschild Black Hole

scholarly journals High-dimensional Schwarzschild black holes in scalar–tensor–vector gravity theory

2021 ◽  
Vol 81 (6) ◽  
Author(s):  
Xin-Chang Cai ◽  
Yan-Gang Miao
Keyword(s):  
Black Hole ◽  
Black Hole Solution ◽  
Emission Rate ◽  
Null Geodesic ◽  
High Dimensional ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Spacetime Dimension ◽  
Schwarzschild Black Hole ◽  
Scalar Waves

AbstractWe obtain a high-dimensional Schwarzschild black hole solution in the scalar–tensor–vector gravity (STVG), and then analyze the influence of parameter $$\alpha $$ α associated with a deviation of the STVG theory from General Relativity on event horizons and Hawking temperature. We calculate the quasinormal mode frequencies of massless scalar field perturbations for the high-dimensional Schwarzschild STVG black hole by using the sixth-order WKB approximation method and the unstable null geodesic method in the eikonal limit. The results show that the increase of parameter $$\alpha $$ α makes the scalar waves decay slowly, while the increase of the spacetime dimension makes the scalar waves decay fast. In addition, we study the influence of parameter $$\alpha $$ α on the shadow radius of this high-dimensional Schwarzschild STVG black hole and find that the increase of parameter $$\alpha $$ α makes the black hole shadow radius increase, but the increase of the spacetime dimension makes the black hole shadow radius decrease. Finally, we investigate the energy emission rate of the high-dimensional Schwarzschild STVG black hole, and find that the increase of parameter $$\alpha $$ α makes the evaporation process slow, while the increase of the spacetime dimension makes the process fast.

scholarly journals Divergent reflections around the photon sphere of a black hole

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Albert Snepppen
Keyword(s):  
Black Hole ◽  
Analytical Solution ◽  
Exponential Family ◽  
Strong Field ◽  
Null Geodesic ◽  
Kerr Black Hole ◽  
Geodesic Equation ◽  
Schwarzschild Black Hole ◽  
Logarithmic Divergence ◽  
Field Limit

AbstractFrom any location outside the event horizon of a black hole there are an infinite number of trajectories for light to an observer. Each of these paths differ in the number of orbits revolved around the black hole and in their proximity to the last photon orbit. With simple numerical and a perturbed analytical solution to the null-geodesic equation of the Schwarzschild black hole we will reaffirm how each additional orbit is a factor $$e^{2 \pi }$$ e 2 π closer to the black hole’s optical edge. Consequently, the surface of the black hole and any background light will be mirrored infinitely in exponentially thinner slices around the last photon orbit. Furthermore, the introduced formalism proves how the entire trajectories of light in the strong field limit is prescribed by a diverging and a converging exponential. Lastly, the existence of the exponential family is generalized to the equatorial plane of the Kerr black hole with the exponentials dependence on spin derived. Thereby, proving that the distance between subsequent images increases and decreases for respectively retrograde and prograde images. In the limit of an extremely rotating Kerr black hole no logarithmic divergence exists for prograde trajectories.

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 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.

scholarly journals GEODESIC STRUCTURE OF THE SCHWARZSCHILD BLACK HOLE IN RAINBOW GRAVITY

2009 ◽  
Vol 24 (18) ◽  
pp. 1443-1451 ◽  
Author(s):  
CARLOS LEIVA ◽  
JOEL SAAVEDRA ◽  
JOSÉ VILLANUEVA
Keyword(s):  
Black Hole ◽  
Test Particle ◽  
Radial Motion ◽  
Schwarzschild Black Hole ◽  
Geodesic Structure

In this paper we study the geodesic structure of the Schwarzschild black hole in rainbow gravity analyzing the behavior of null and time-like geodesic. We find that the structure of the geodesics essentially does not change when the semiclassical effects are included. However, we can distinguish different scenarios if we take into account the effects of rainbow gravity. Depending on the type of rainbow functions under consideration, inertial and external observers see very different situations in radial and non-radial motion of a test particle.

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