Polar perturbations in Kantowski-Sachs spacetimes and hybrid quantum cosmology

Abstract

Increasing attention has been recently devoted to the study of Kantowski-Sachs spacetime as a way to explore the interior of a Schwarzschild black hole. In this work, we construct a Hamiltonian formulation for polar perturbations of this spacetime in the presence of a perturbative massless scalar field. Our analysis is based on a truncated action at quadratic order in perturbations. Both background and perturbative degrees of freedom are treated dynamically, forming a combined system that is endowed with the canonical structure obtained from our truncated action. First-order perturbations of the metric and the matter field are described using perturbative gauge invariants, linear perturbative constraints, and their corresponding canonical variables. For the quantum description, we adopt a hybrid approach where the background is quantized with loop quantum gravity techniques and the perturbations with conventional quantum field methods.

22 pages

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Cited by in corpus (3)

• Master variables and Darboux symmetry for axial perturbations of the exterior and interior of black hole spacetimes
• Hamiltonian formalism, master functions and Darboux transformations for perturbed (interiors and exteriors of) nonrotating black holes
• Effective Regge-Wheeler equations of a hybrid loop quantum black hole