Remarks on the distributional Schwarzschild geometry

Details Remarks on the distributional Schwarzschild geometry Remarks on the distributional Schwarzschild geometry

2001-12-19

arxiv.org/abs/gr-qc/0112047v1

J.Math.Phys. 43 (2002) 1493-1508

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages, revtex4, to appear in JMP

Scientific paper

This work is devoted to a mathematical analysis of the distributional Schwarzschild geometry. The Schwarzschild solution is extended to include the singularity; the energy momentum tensor becomes a delta-distribution supported at r=0. Using generalized distributional geometry in the sense of Colombeau's (special) construction the nonlinearities are treated in a mathematically rigorous way. Moreover, generalized function techniques are used as a tool to give a unified discussion of various approaches taken in the literature so far; in particular we comment on geometrical issues.

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