Quantum gravity predictions for black hole interior geometry

Abstract

In a previous work we derived an effective Hamiltonian constraint for the Schwarzschild geometry starting from the full loop quantum gravity Hamiltonian constraint and computing its expectation value on coherent states sharply peaked around a spherically symmetric geometry. We now use this effective Hamiltonian to study the interior region of a Schwarzschild black hole, where a homogeneous foliation is available. Descending from the full theory, our effective Hamiltonian, though still bearing the well known ambiguities of the quantum Hamiltonian operator, preserves all relevant information about the fundamental discreteness of quantum space. This allows us to have a uniform treatment for all quantum gravity holonomy corrections to spatially homogeneous geometries, unlike the minisuperspace loop quantization models in which the effective Hamiltonian is postulated. We show how, for several geometrically and physically well motivated choices of coherent states, the classical black hole singularity is replaced by a homogeneous expanding Universe. The resultant geometries have no significant deviations from the classical Schwarzschild geometry in the pre-bounce sub-Planckian curvature regime, evidencing the fact that large quantum effects are avoided in these models. In all cases, we find no evidence of a white hole horizon formation. However, various aspects of the post-bounce effective geometry depend on the choice of quantum states.