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 VOROS PRODUCT AND NONCOMMUTATIVE INSPIRED BLACK HOLES

2013 ◽  
Vol 28 (09) ◽  
pp. 1350030
Author(s):  
SUNANDAN GANGOPADHYAY
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Extremal Point ◽  
De Sitter ◽  
Schwarzschild Black Hole ◽  
Standard Identity ◽  
Schwarzschild Geometry ◽  
Area Law

We emphasize the importance of the Voros product in defining the noncommutative (NC) inspired black holes. The computation of entropy for both the noncommutative inspired Schwarzschild and Reissner–Nordström (RN) black holes show that the area law holds up to order [Formula: see text]. The leading correction to the entropy (computed in the tunneling formalism) is shown to be logarithmic. The Komar energy E for these black holes is then obtained and a deviation from the standard identity E = 2STH is found at the order [Formula: see text]. This deviation leads to a nonvanishing Komar energy at the extremal point TH = 0 of these black holes. The Smarr formula is finally worked out for the NC Schwarzschild black hole. Similar features also exist for a de Sitter–Schwarzschild geometry.

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.

scholarly journals SPACE–TIMES WITH INTEGRABLE SINGULARITY: BLACK–WHITE HOLES AND ASTROGENIC UNIVERSES

2013 ◽  
Vol 28 (02) ◽  
pp. 1350007 ◽  
Author(s):  
VLADIMIR N. LUKASH ◽  
VLADIMIR N. STROKOV
Keyword(s):  
Black Hole ◽  
Gravitational Field ◽  
Phenomenological Approach ◽  
Space Time ◽  
Schwarzschild Black Hole ◽  
White Hole ◽  
Black Hole Singularity

We use the phenomenological approach to study properties of space–time in the vicinity of the Schwarzschild black-hole singularity. Requiring finiteness of the Schwarzschild-like metrics we come to the notion of integrable singularity that is, in a sense, weaker than the conventional singularity and allows the (effective) matter to pass to the white-hole region. This leads to a possibility of generating a new universe there. Thanks to the gravitational field of the singularity, this universe is already born highly inflated ("singularity-induced inflation") before the ordinary inflation starts.

scholarly journals Time delay of radiation from pulsar in a binary system that moves in field of Schwarzschild black hole

2017 ◽  
Vol 57 (2) ◽  
Author(s):  
Stanislav Komarov ◽  
Alexander Gorbatsievich ◽  
Alexander Tarasenko
Keyword(s):  
Black Hole ◽  
Gravitational Field ◽  
Time Delay ◽  
Binary System ◽  
Binary Star ◽  
Schwarzschild Black Hole ◽  
External Gravitational Field ◽  
Compact Binary

A compact binary star that moves in a strong external gravitational field of a Schwarzschild black hole is considered. Decomposition of the redshift into a series with respect to the size of the binary system is obtained. This expression is used to calculate the redshift for a model binary system. Possible application of the results is discussed.

scholarly journals Absence of Singularity in Schwarzschild Metric in the Vector Model for Gravitational Field

2012 ◽  
Vol 18 (3) ◽  
pp. 175-184
Author(s):  
Vo Van On
Keyword(s):  
Black Hole ◽  
Gravitational Field ◽  
General Theory ◽  
Space Time ◽  
Symmetric Body ◽  
Vector Model ◽  
Spherically Symmetric ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Schwarzschild Metric

In this paper, based on the vector model for gravitational field we deduce an equation to determinate the metric of space-time. This equation is similar to equation of Einstein. The metric of space-time outside a static spherically symmetric body is also determined. It gives a small supplementation to the Schwarzschild metric in General theory of relativity but the singularity does not exist. Especially, this model predicts the existence of a new universal body after a black hole.

scholarly journals The Mirror Reversal Mechanism on Black Hole Collapse and Singularity Eruption in Cosmic Continuum

2021 ◽  
Author(s):  
Xijia Wang
Keyword(s):  
Black Hole ◽  
Gravitational Field ◽  
Schwarzschild Black Hole ◽  
Strong Gravitational Field ◽  
Conversion Point ◽  
Mirror Reversal ◽  
System Collapse ◽  
Starting Point ◽  
Reversal Mechanism ◽  
Schwarzschild Radius

Abstract In Cosmic continuum, the cosmic system collapse into a Schwarzschild black hole under the action of a strong gravitational field, and the Planck spheres at the center of the black hole continues to collapse into dark mass bodies, forming dark celestial body and singularity. The Schwarzschild radius is the upper limit of a black hole, and the Planck sphere is the lower limit of a black hole. The singularity is the conversion point between the old and new cosmic systems. The singularity erupts the Planck spheres under the action of a strong gravitational field, and the Planck spheres expands outward to form a new cosmic system. The Planck sphere is both the end of the old cosmic system and the starting point of the new cosmic system. The black hole collapse and the singularity eruption are mirror images of each other. The Planck sphere is the front of the mirror, and the singularity is the back of the mirror.

scholarly journals Analog Schwarzschild Black Hole from a Nonisentropic Fluid

Universe ◽  
2021 ◽  
Vol 7 (11) ◽  
pp. 413
Author(s):  
Neven Bilić ◽  
Hrvoje Nikolić
Keyword(s):  
Black Hole ◽  
Speed Of Sound ◽  
Speed Of Light ◽  
Schwarzschild Black Hole ◽  
Flat Spacetime ◽  
Schwarzschild Geometry ◽  
Relativistic Fluid ◽  
Hole Geometry

We study the conditions under which an analog acoustic geometry of a relativistic fluid in flat spacetime can take the same form as the Schwarzschild black hole geometry. We find that the speed of sound must necessarily be equal to the speed of light. Since the speed of the fluid cannot exceed the speed of light, this implies that analog Schwarzschild geometry necessarily breaks down behind the horizon.

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

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