Authors: M O Katanaev
Publish Date: 2013/07/24
Volume: 45, Issue: 10, Pages: 1861-1875
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 neighborhoodThe author is grateful to I V Volovich A K Gushchin Yu N Drozhzhinov B I Zavialov who died last year and V P Mikhailov for discussions and valuable comments The work is supported by RFFI Grants 110100828a and 130112424ofim the Program for Supporting Leading Scientific Schools Grant NSh292820121 and the Program “Modern problems of theoretical mathematics” by RAS
Keywords: