Effective Regge-Wheeler equations of a hybrid loop quantum black hole

TL;DR

This paper derives effective gauge-invariant gravitational perturbation equations for a quantum-corrected black hole interior within hybrid loop quantum gravity, enabling analysis of quantum effects on gravitational wave propagation.

Contribution

It introduces a novel set of Regge-Wheeler equations incorporating quantum geometry corrections in a hybrid loop quantum gravity framework.

Findings

Modified Regge-Wheeler equations with quantum corrections

Framework for studying gravitational wave propagation in quantum black holes

Explicit quantum Hamiltonian constraint implementation

Abstract

A set of effective equations for the gauge-invariant gravitational perturbations in the interior of a spherically symmetric, non-rotating black hole is derived within the framework of hybrid loop quantum cosmology. The quantum zero-mode of the Hamiltonian constraint, obtained from a perturbative gauge-invariant canonical analysis, is explicitly imposed on a class of quantum states whose wavefunctions factorize into a background and a perturbative part, related through a geometric relational variable. These states naturally describe regimes with small perturbative backreaction and lead to an effective Hamiltonian and associated dynamics for the perturbations. The resulting equations take the form of Regge-Wheeler equations modified by expectation values of the quantum black hole geometry, providing a clear characterization of quantum corrections to the classical description of the black hole interior. This framework opens the way to investigating hybrid loop quantum gravity effects in the propagation of gravitational waves.