Gravitational field of massive point particle in general relativity

TLDR: In this article, a description of the static spherically symmetric space-times with point singularity at the center and vacuum outside the singularity is given, and a new physical class of gauges are proposed, in this way achieving a correct description of a point mass source in general relativity.

Abstract: Using various gauges of the radial coordinate we give a description of the static spherically symmetric space-times with point singularity at the center and vacuum outside the singularity. We show that in general relativity (GR) there exist innitely many such solutions to the Einstein equations which are physically dieren t and only some of them describe the gravitational eld of a single massive point particle. In particular, we show that the widespread Hilbert’s form of Schwarzschild solution does not solve the Einstein equations with a massive point particle’s stress-energy tensor. Novel normal coordinates for the eld and a new physical class of gauges are proposed, in this way achieving a correct description of a point mass source in GR. We also introduce a gravitational mass defect of a point particle and determine the dependence of the solutions on this mass defect. In addition we give invariant characteristics of the physically and geometrically dieren t classes of spherically symmetric static space-times created by one point mass.