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

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.

References in corpus (1)

• Inverse problems for quadratic derivative nonlinear wave equations

Cited by in corpus (5)

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• Uniqueness and stability of an inverse problem for a semi-linear wave equation
• An Inverse Problem for the Relativistic Boltzmann Equation
• Nonlinear interaction of three impulsive gravitational waves I: main result and the geometric estimates
• Determining a nonlinear hyperbolic system with unknown sources and nonlinearity