Extension of the Schwarzschild Solution
to the Case of Localized Fluid Matter
I: Derivation and Properties

Jorge L. deLyra¹

Department of Mathematical Physics, Physics Institute, University of São Paulo

June 25, 2019

Abstract:

We work out, mostly but not completely by analytic methods, the solution of the Einstein gravitational field equation in the presence of a localized fluid-matter energy-momentum tensor, for a situation in which there is spherical symmetry, independence of the time, and a definite homogeneous equation of state. In this work we follow the arguments given, and use the results obtained and the conventions adopted in Dirac's marvelous little book on General Relativity [#!DiracGravity!#]. We establish some of the main properties, and discuss in a general way some other properties, of the two-parameter class of solutions presented, including the nature of the geometry within the matter distribution and the possibility of the formation of event horizons.