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International conference MIAN-Institute of mathematics of China Academy of Science on Complex Analysis and Mathematical Physics
October 15, 2014 10:00–10:50, Beijing, China, Institute of Mathematics, Chinese Academy of Sciences

Point massive particle in General Relativity

M. O. Katanaev

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. We prove that the Schwarzschild solution in isotropic coordinates is the asymptotically at 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.