scholarly journals General Teleparallel Modifications of Schwarzschild Geometry

2021 ◽  
Author(s):  
Sebastian Bahamonde ◽  
Christian Pfeifer
Keyword(s):  
Schwarzschild Geometry

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 EXTERIOR GRAVITATIONAL PERTURBATION ON GENERALIZED SCHWARZSCHILD GEOMETRY

2000 ◽  
Vol 49 (6) ◽  
pp. 1031
Author(s):  
LI XIN-ZHOU ◽  
YUAN NING-YI ◽  
LIU DAO-JUN ◽  
HAO JIAN-GANG
Keyword(s):  
Gravitational Perturbation ◽  
Schwarzschild Geometry

Light Inextensible Strings (Thread) Under Tension in the Schwarzschild Geometry

2021 ◽  
Vol 03 (02) ◽  
pp. 2150005
Author(s):  
Robin K. S. Hankin
Keyword(s):  
Free Fall ◽  
Computer Algebra Systems ◽  
Lagrange Equations ◽  
Schwarzschild Metric ◽  
Schwarzschild Geometry ◽  
Homework Problem ◽  
Straight Line ◽  
Taut Strings ◽  
Proper Length ◽  
Insight Into

Light inextensible string under tension is a stalwart feature of elementary physics. Here I show how considering such a string in the vicinity of a black hole, with the help of computer algebra systems, can generate insight into the Schwarzschild geometry in the context of an undergraduate homework problem. Light taut strings minimize their proper length, given by integrating the spatial component of the Schwarzschild metric along the string. The path itself is given by straightforward numerical solution to the Euler–Lagrange equations. If the string is entirely outside the event horizon, its closest approach to the singularity is tangential. At this point the string is visibly curved, surely a memorable and informative insight. The geometry of the Schwarzschild metric induces some interesting nonlocal phenomena: if the distance of closest approach is less than about [Formula: see text], the string self-intersects, even though it is everywhere under tension. Light taut strings furnish a third interpretation of the concept “straight line”, the other two being null geodesics and free-fall world lines. All the software used is available under the GPL.1

scholarly journals Isotropic Gravastar Model in Rastall Gravity

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
G. Abbas ◽  
K. Majeed
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Analytical Solutions ◽  
Thin Shell ◽  
Graphical Analysis ◽  
Stiff Fluid ◽  
Matter Distribution ◽  
The Third ◽  
Schwarzschild Geometry ◽  
Third Phase

In the present paper, we have introduced a new model of gravastar with an isotropic matter distribution in Rastall gravity by the Mazur–Mottola (2004) mechanism. Mazur–Mottola approach is about the construction of gravastar which is predicted as an alternative to black hole. By following this convention, we define gravastar in the form of three phases. The first one is an interior phase which has negative density; the second part consists of thin shell comprising ultrarelativistic stiff fluid for which we have discussed the length, energy, and entropy. By the graphical analysis of entropy, we have shown that our proposed thin shell gravastar model is potentially stable. The third phase of gravastar is defined by the exterior Schwarzschild geometry. For the interior of gravastar, we have found the analytical solutions free from any singularity and the event horizon in the framework of Rastall gravity.

On the symmetry and conservation law classification of the de Sitter–Schwarzschild metric and the corresponding wave and Klein–Gordon equations

2020 ◽  
Vol 17 (11) ◽  
pp. 2050172
Author(s):  
Ashfaque H. Bokhari ◽  
A. H. Kara ◽  
F. D. Zaman ◽  
B. B. I. Gadjagboui
Keyword(s):  
Conservation Laws ◽  
Conservation Law ◽  
De Sitter ◽  
Killing Vectors ◽  
Schwarzschild Geometry ◽  
Klein Gordon ◽  
Spacetime Metric ◽  
Variational Symmetries ◽  
Symmetry And Conservation Law

The main purpose of this work is to focus on a discussion of Lie symmetries admitted by de Sitter–Schwarzschild spacetime metric, and the corresponding wave or Klein–Gordon equations constructed in the de Sitter–Schwarzschild geometry. The obtained symmetries are classified and the variational (Noether) conservation laws associated with these symmetries via the natural Lagrangians are obtained. In the case of the metric, we obtain additional variational ones when compared with the Killing vectors leading to additional conservation laws and for the wave and Klein–Gordon equations, the variational symmetries involve less tedious calculations as far as invariance studies are concerned.

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