An Extension of Schwarzschild Space to r=0

Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology

Scientific paper

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16 pages, no figure, some errors are corrected, two sections on tidal forces and Riemann scalar invariant are added. To appear

Scientific paper

10.1238/Physica.Regular.064a0041

A more rigorous treatment of the Schwarzschild metric by making use of the energy-momentum tensor of a single point particle as source term shows that $g_{00}=-\{1-\frac{2GM}{c^2r}-\frac{8G^2 M^2}{c^4 r^2}(\theta (r)-1)\}\exp [2(\theta (r)-1)]$ $g_{rr}=\{1-\frac{2GM}{c^2r}-\frac{8G^2 M^2}{c^4 r^2}(\theta (r)-1)\}^{-1}$ The existence of a discontinuity at r=0 leads to an infinite repulsive force that will change the ultimate fate of a free fall test particle to a bouncing state.

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