The Black Hole

Black holes are solutions of the general relativistic field equations. The solutions for motions of test particles for a non-rotating, spherical symmetric black hole are given by equ. 1 and 2 (cf. Sect. 9.1 of [19]).

Here V2 (r) = ( 1 - 2GM/rc2)(1 + h2 /r2) is the effective potential, h is the angular momentum of a test particle in the gravitational potential, t is the time measured by a distant observer (the distance r to the black hole approaches infinity), M is the mass of the black hole and s gives the time dependent on the strength of the gravitational field. The term E describes the total energy of a test particle per unit mass, G is the gravitational constant and c is the velocity of light.

follows V —> 0,d —> «> ds and a singularity results. The term RS is therefore called the event horizon or Schwarzschild radius. Below RS radiation and particles cannot leave the blackhole, as RS is the radius of the maximum allowed escape velocity vescape = (2GM/Rs)1/2 = c.

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