Quantum field theory of black hole perturbations with backreaction IV: spherically symmetric 2nd order Einstein–Maxwell sector in generalised gauges

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 Painlevé gauge and confirmed consistency with previous approaches. In the analysis, we defined the gauge invariant variables non-perturbatively and took backreaction effects explicitly into account. In this paper, as a non-trivial consistency check, we generalize the results and show that a similar analysis is possible for other choices of gauge for the background variables. 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.