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Remarks on the distributional Schwarzschild geometry

J. Mark Heinzle·Roland Steinbauer
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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.

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J. Mark Heinzle, Roland Steinbauer. 2001-12-19. Remarks on the distributional Schwarzschild geometry. https://doi.org/10.1063/1.1448684

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