Master functions and hybrid quantization of perturbed nonrotating black hole interiors

Abstract Master functions of black holes (BHs) are fundamental tools in gravitational-wave physics and are typically derived within a Lagrangian framework. For the interior region of an uncharged and nonrotating BH, one can instead construct a perturbative Hamiltonian description starting from the Kantowski–Sachs spacetime. 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 BH analyses. Once a consistent Hamiltonian description for their canonical counterparts is obtained, a hybrid quantization of the master functions follows naturally.