Quantum gravity predictions for black hole interior geometry. (arXiv:1904.12412v1 [gr-qc])
<a href="http://arxiv.org/find/gr-qc/1/au:+Alesci_E/0/1/0/all/0/1">Emanuele Alesci</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Bahrami_S/0/1/0/all/0/1">Sina Bahrami</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Pranzetti_D/0/1/0/all/0/1">Daniele Pranzetti</a>
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 preserves all relevant information about the graph
structure of quantum space and encapsulates all dominant quantum gravity
corrections to spatially homogeneous geometries at the effective level. It
carries significant differences from the effective Hamiltonian postulated in
the context of minisuperspace loop quantization models in the previous
literature. We show how, for two 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 both cases, we find no evidence of a while hole
horizon formation However, various aspects of the post-bounce effective
geometry depend on the choice of quantum states.
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 preserves all relevant information about the graph
structure of quantum space and encapsulates all dominant quantum gravity
corrections to spatially homogeneous geometries at the effective level. It
carries significant differences from the effective Hamiltonian postulated in
the context of minisuperspace loop quantization models in the previous
literature. We show how, for two 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 both cases, we find no evidence of a while hole
horizon formation However, various aspects of the post-bounce effective
geometry depend on the choice of quantum states.
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