Well-posed formulation of Einstein-Maxwell effective field theory

TL;DR

This paper demonstrates that Einstein-Maxwell theories with certain higher derivative corrections can be formulated to have a well-posed initial value problem using a modified harmonic gauge, ensuring mathematical consistency.

Contribution

It shows how to use field redefinitions and a modified gauge to achieve well-posedness in higher derivative Einstein-Maxwell theories.

Findings

Well-posed initial value formulation for Einstein-Maxwell with higher derivatives.

Modified harmonic gauge enables stable evolution equations.

Corrections are manageable when higher derivative terms are small.

Abstract

We consider the well-posedness of the initial value problem for Einstein-Maxwell theory modified by higher derivative effective field theory corrections. Field redefinitions can be used to bring the leading parity-symmetric 4-derivative corrections to a form which gives second order equations of motion. We show that a recently introduced "modified harmonic" gauge condition can be used to obtain a formulation of these theories which admits a well-posed initial value problem when the higher derivative corrections to the equations of motion are small.