Quantum evolution of black hole initial data sets: Foundations

TL;DR

This paper develops a quantum gravity formalism to evolve spherically symmetric black hole initial data, deriving an effective Hamiltonian for quantum black hole geometries within a loop gravity framework.

Contribution

It introduces a new approach combining partial gauge fixing and semiclassical states in quantum reduced loop gravity to model black hole evolution.

Findings

Derived an effective Hamiltonian for quantum black hole evolution.

Established a formalism for evolving classical black hole data quantum mechanically.

Extended loop quantum cosmology techniques to black hole spacetimes.

Abstract

We construct a formalism for evolving spherically symmetric black hole initial data sets within a canonical approach to quantum gravity. This problem can be formulated precisely in quantum reduced loop gravity, a framework which has been successfully applied to give a full theory derivation of loop quantum cosmology. We extend this setting by implementing a particular choice of partial gauge which is then used to select a kinematical Hilbert space where the symmetry reduction is imposed through semiclassical states. The main result of this investigation is an effective Hamiltonian that can be used to solve for quantum black hole geometries by evolving classical black hole initial data sets.