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 δdistribution 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:grqc/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
 EPrint:
 13 pages, revtex4, to appear in JMP