Master functions and hybrid quantization of perturbed nonrotating black hole interiors

TL;DR

This paper develops a Hamiltonian framework for black hole interiors and exteriors, linking perturbative invariants with master functions, and introduces a hybrid quantization approach for these functions to advance quantum gravity research.

Contribution

It introduces a Hamiltonian formulation for black hole perturbations that connects with master functions and enables hybrid quantization, offering a new perspective beyond traditional Lagrangian methods.

Findings

Established a correspondence between canonical invariants and master functions.

Extended the Hamiltonian approach to the exterior black hole region.

Proposed a hybrid quantization scheme for master functions.

Abstract

Master functions of black holes are fundamental tools in gravitational-wave physics and are typically derived within a Lagrangian framework. Starting from the Kantowski-Sachs geometry, one can instead construct a perturbative Hamiltonian description for the interior region of an uncharged and nonrotating black hole. This approach provides a complementary perspective and enables a quantum treatment of the background geometry and its perturbations. In this work, we extend the application of this formulation to the exterior region and establish a correspondence between the perturbative invariants of the canonical approach and the master functions commonly used in black hole analyses. Once a consistent Hamiltonian description for their canonical counterparts is obtained, a hybrid quantization of the master functions follows naturally.