Determination of vacuum space-times from the Einstein-Maxwell equations

TL;DR

This paper demonstrates that vacuum space-time structures can be uniquely determined by measuring gravitational perturbations generated through nonlinear interactions of electromagnetic waves, using inverse problem techniques.

Contribution

It introduces a method to recover vacuum space-time geometry from electromagnetic and gravitational wave interactions via inverse problem analysis.

Findings

Gravitational waves can be generated from electromagnetic wave interactions.

Vacuum space-time can be reconstructed from local measurements.

The method applies to the largest region accessible by the waves.

Abstract

We study inverse problems for the Einstein-Maxwell equations. We prove that it is possible to generate gravitational waves from the nonlinear interactions of electromagnetic waves. By sending electromagnetic waves from a neighborhood of a freely falling observer and taking measurements of the gravitational perturbations in the same neighborhood, one can determine the vacuum space-time structure up to diffeomorphisms in the largest region where these waves can travel to from the observer and return.