Motion in central gravitational field with Schwarzschild metric as a non-holonomic system with non-linear constraint: Geometrical setting

2019 ◽  
Vol 114 ◽  
pp. 21-26 ◽  
Author(s):  
Michal Čech ◽  
Jana Musilová
Keyword(s):  
Gravitational Field ◽  
Linear Constraint ◽  
Holonomic System ◽  
Schwarzschild Metric ◽  
Non Linear ◽  
Central Gravitational Field

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.

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