Threshold for strong hyperbolicity of modified-harmonic formulations with higher-derivative corrections

Determine rigorous quantitative conditions or bounds on the size of the higher-derivative contributions in modified-harmonic-gauge formulations of gravitational effective field theories—specifically, in the Einstein–Maxwell effective field theory—under which the equations remain strongly hyperbolic and the initial value problem stays well-posed, and identify when strong hyperbolicity fails as these contributions grow.

Background

The thesis proves that the modified harmonic gauge yields a strongly hyperbolic, and hence well-posed, initial value formulation of the Einstein–Maxwell effective field theory when the higher-derivative terms are small (weak coupling/regime of validity).

However, the analysis does not provide a quantitative boundary for how large the higher-derivative terms can be before strong hyperbolicity and well-posedness break down. Establishing such a threshold is important both for mathematical control and for assessing the robustness of simulations and theoretical predictions beyond the strict weak-coupling regime.