Quantum gravity predictions for black hole interior geometry

Understand

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.