Remarks on the distributional Schwarzschild geometry

Abstract

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.

13 pages, revtex4, to appear in JMP

References in corpus (2)

• On the foundations of nonlinear generalized functions I
• Distributional Sources in General Relativity: two point-like examples revisited

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