Finding and using exact solutions of the Einstein equations

TL;DR

This paper reviews the historical development of methods for finding exact solutions to Einstein's field equations and discusses their significance in advancing general relativity.

Contribution

It provides a comprehensive overview of the evolution of solution-finding techniques and highlights their impact on the field of general relativity.

Findings

Invariant methods became dominant since the 1950s.

Exact solutions have significantly contributed to the development of general relativity.

Solutions have been applied to both mathematical and physical problems.

Abstract

The evolution of the methods used to find solutions of Einstein's field equations during the last 100 years is described. Early papers used assumptions on the coordinate forms of the metrics. Since the 1950s more invariant methods have been deployed in most new papers. The uses to which the solutions found have been put are discussed, and it is shown that they have played an important role in the development of many aspects, both mathematical and physical, of general relativity.