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.
- Publication:
-
Journal of Mathematical Physics
- Pub Date:
- March 2002
- DOI:
- 10.1063/1.1448684
- arXiv:
- arXiv:gr-qc/0112047
- Bibcode:
- 2002JMP....43.1493H
- Keywords:
-
- 04.20.Jb;
- 04.20.Gz;
- Exact solutions;
- Spacetime topology causal structure spinor structure;
- General Relativity and Quantum Cosmology;
- Mathematical Physics
- E-Print:
- 13 pages, revtex4, to appear in JMP