# The spherically symmetric gravitational field

## TL;DR

This paper derives a comprehensive general solution for spherically symmetric gravitational fields in an isotropic, flat universe, unifying various classical solutions and introducing new methods for generating solutions involving dust, radiation, and explosive phenomena.

## Contribution

It presents a unified general solution in General Relativity for spherically symmetric fields, including new solution-generating methods and exact solutions for complex astrophysical scenarios.

## Key findings

- Unified general solution encompasses Schwarzschild, Friedmann, Einstein-de Sitter cases.
- New method for generating infinite Tolman's-like solutions.
- Exact solutions for dust clouds in radiation-filled expanding universe.

## Abstract

The general solution of the system of General Relativity equations has been found for isotropic Universe with the flat spatial distribution and synchronized time taking into account a perfect dust and the cosmological constant. Schwarzschild, Friedmann and Einstein-de Sitter solutions (as well as all of their fusion with each other) are special cases of the found general solution. A method of generating an infinite number of Tolman's like solutions has been found. Exact solutions has been found for the spherically symmetric gravitational field of perfect dust clouds in the expanding Universe filled with radiation. A system of ordinary differential equations has been obtained for the spherically symmetric gravitational field of perfect dust clouds in the expanding Universe filled with radiation and nonrelativistic gas. A system of equations has been obtained for the spherically symmetric gravitational field of ultrarelativistic celestial body explosion (supernova, quasar). The problem of a negative density of a perfect dust cloud in General Relativity has been considered.