Exact Vacuum Solutions to the Einstein Equation

TL;DR

This paper introduces a systematic framework for deriving exact vacuum solutions to Einstein's equations by reducing them to simpler 2D Laplace-like and divergence equations, facilitating their resolution.

Contribution

It provides a novel canonical form-based method to obtain a series of exact solutions to Einstein's vacuum equations, simplifying the solving process.

Findings

Framework reduces Einstein equations to 2D Laplace-like equations.

Enables systematic derivation of exact vacuum solutions.

Simplifies the resolution process for Einstein's equations.

Abstract

In this paper, we present a framework for getting a series of exact vacuum solutions to the Einstein equation. This procedure of resolution is based on a canonical form of the metric. According to this procedure, the Einstein equation can be reduced to some 2-dimensional Laplace-like equations or rotation and divergence equations, which are much convenient for the resolution.