Quantum Field Theory of Black Hole Perturbations with Backreaction IV. Spherically symmetric 2nd order Einstein-Maxwell sector in generalised gauges

TL;DR

This paper extends the reduced phase space analysis of spherically symmetric Einstein-Maxwell perturbations to more general gauges, maintaining the structure of the Hamiltonian with Regge-Wheeler and Zerilli potentials.

Contribution

It generalizes previous gauge choices in the analysis of black hole perturbations, demonstrating the robustness of the Hamiltonian structure across different gauges.

Findings

Hamiltonian retains Regge-Wheeler and Zerilli potentials

Analysis compatible with a broader class of gauges

Confirms consistency with previous approaches

Abstract

In previous papers of this series we analysed the reduced phase space approach to perturbations of Einstein-Maxwell theory to second order around spherically symmetric backgrounds in the Gullstrand Painlev\'e Gauge and confirmed consistency with previous approaches. In this paper we generalize this result and show that the analysis can be performed in gauges for the background variables compatible with the Gullstrand Painlev\'e gauge. We obtain the same structure for the reduced Hamiltonian that contains the well known Regge-Wheeler and Zerilli potentials. Possible applications of this generalization are discussed.