
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 energymomentum 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.
DOI:
https://doi.org/10.1007/s1071401315643
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Article Received: 30.03.2013 Accepted:07.07.2013
Language: English
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