Is general relativity `essentially understood' ?

TL;DR

While general relativity is well-understood in many regimes, the paper highlights the limited understanding of highly dynamical, strong field solutions and emphasizes the need for new methods to analyze Einstein's equations.

Contribution

The paper reviews the current state of understanding of Einstein's field equations and discusses open problems and recent progress in analyzing complex solutions.

Findings

Significant progress in understanding solutions to Einstein's equations

Limited understanding of highly dynamical, strong field regimes

Need for new analytical and numerical methods

Abstract

The content of Einstein's theory of gravitation is encoded in the properties of the solutions to his field equations. There has been obtained a wealth of information about these solutions in the ninety years the theory has been around. It led to the prediction and the observation of physical phenomena which confirm the important role of general relativity in physics. The understanding of the domain of highly dynamical, strong field configurations is, however, still quite limited. The gravitational wave experiments are likely to provide soon observational data on phenomena which are not accessible by other means. Further theoretical progress will require, however, new methods for the analysis and the numerical calculation of the solutions to Einstein's field equations on large scales and under general assumptions. We discuss some of the problems involved, describe the status of the field and recent results, and point out some open problems.