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Gen. Relativity Gravitation, 2013, Volume 45, Issue 10, Pages 1861–1875 (Mi grg1)  

Point massive particle in general relativity

M. O. Katanaev

Steklov Mathematical Institute, ul. Gubkina, 8, Moscow 119991, Russia

Abstract: It is well known that the Schwarzschild solution describes the gravitational field outside compact spherically symmetric mass distribution in General Relativity. In particular, it describes the gravitational field outside a point particle. Nevertheless, what is the exact solution of Einstein’s equations with $\delta$-type source corresponding to a point particle is not known. In the present paper, we prove that the Schwarzschild solution in isotropic coordinates is the asymptotically flat static spherically symmetric solution of Einstein’s equations with $\delta$-type energy-momentum tensor corresponding to a point particle. Solution of Einstein’s equations is understood in the generalized sense after integration with a test function. Metric components are locally integrable functions for which nonlinear Einstein’s equations are mathematically defined. The Schwarzschild solution in isotropic coordinates is locally isometric to the Schwarzschild solution in Schwarzschild coordinates but differs essentially globally. It is topologically trivial neglecting the world line of a point particle. Gravity attraction at large distances is replaced by repulsion at the particle neighborhood.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00828-a
13-01-12424-ofi-m
Ministry of Education and Science of the Russian Federation NSh-2928.2012.1
Russian Academy of Sciences - Federal Agency for Scientific Organizations
The work is supported by RFFI (Grants 11-01-00828-a and 13-01-12424-ofi-m), the Program for Supporting Leading Scientific Schools (Grant NSh-2928.2012.1), and the Program “Modern problems of theoretical mathematics” by RAS.


DOI: https://doi.org/10.1007/s10714-013-1564-3


Bibliographic databases:

Document Type: Article
Received: 30.03.2013
Accepted:07.07.2013
Language: English

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