TITLE:
Spherically Symmetric Problem of General Relativity for a Fluid Sphere
AUTHORS:
Valery V. Vasiliev, Leonid V. Fedorov
KEYWORDS:
General Relativity, Spherically Symmetric Problem, Fluid Sphere
JOURNAL NAME:
Journal of Modern Physics,
Vol.15 No.4,
March
18,
2024
ABSTRACT: The paper is devoted to a spherically symmetric problem of General Relativity (GR) for a fluid sphere. The problem is solved within the framework of a special geometry of the Riemannian space induced by gravitation. According to this geometry, the four-dimensional Riemannian space is assumed to be Euclidean with respect to the space coordinates and Riemannian with respect to the time coordinate. Such interpretation of the Riemannian space allows us to obtain complete set of GR equations for the external empty space and the internal spaces for incompressible and compressible perfect fluids. The obtained analytical solution for an incompressible fluid is compared with the Schwarzchild solution. For a sphere consisting of compressible fluid or gas, a numerical solution is presented and discussed.