Invariant Solutions for the Einstein Field Equation

TL;DR

This paper introduces a method to generate numerous solutions for Einstein's field equations in static spacetimes with perfect fluid matter, characterizing symmetric and conformally flat spatial factors, and provides some exact solutions.

Contribution

The paper presents a novel method for producing an infinite set of solutions for Einstein's equations in specific static spacetimes, expanding the solution space.

Findings

Characterization of symmetric static spacetimes with conformally flat spatial factors.

Development of a method to generate infinite solutions for Einstein's equations.

Provision of explicit exact solutions using the method.

Abstract

In this paper we provide a method capable of producing an infinite number of solutions for Einstein's equation on static spacetimes with perfect fluid as a matter field. All spacetimes of this type which are symmetric with respect to a given group of translations and whose spatial factor is conformally flat, are characterized. We use this method to give some exact solutions of the referred equation.