Scalar Vacuum Polarization in Loop Quantum Gravity Black Holes
Abstract
A quantum macroscopic ``Kruskal'' black hole solution that incorporates quantum geometry effects has been derived in \chg{loop quantum gravity} as the counterpart to the classical Schwarzschild solution with a distinct imprint outside the event horizon, even at scales much larger than the Planck length. This resulting black hole quantum geometry is supported by an effective energy density of quantum origin, outside the horizon, which prevents asymptotic flatness at large distances and confines massive particles to finite radii, thereby preventing their escape to infinity. In this work\chg{,} we adapt to these solutions the extended Anderson-Candelas-Christensen-DeWitt approach to compute the quantum vacuum polarization in order to provide an accurate measure of the quantum activity around these black holes. We carry out a numerical implementation of the formalism and present, to our knowledge for the first time, the scalar vacuum polarization ⟨ϕ2⟩ exterior to this quantum-corrected geometry. We find that the quantum-gravity exponent ε enhances the near-horizon polarization and induces, farther out, a small negative tail that we identify---through a parameter-free \chg{DeWitt-Schwinger} comparison---with the field's response to the nonzero curvature of the background (absent for Ricci-flat Schwarzschild). The correction scales linearly with ε, the parameter tracking the quantum gravitational corrections, so that\chg{,} for astrophysically realistic (i.e., tiny) ε, the result is numerically indistinguishable from Schwarzschild. The calculation furnishes a consistency check on the quantum activity around these solutions, the fluctuations tracking the local curvature without anomalous growth in the exterior.
Versions
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BibTeX
@misc{flachi2026scalar,
title = {{Scalar Vacuum Polarization in Loop Quantum Gravity Black Holes}},
author = {Antonino Flachi and Marco Pasini},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2606.29307},
eprint = {2606.29307},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.29307},
}
RIS
TY - UNPB
TI - Scalar Vacuum Polarization in Loop Quantum Gravity Black Holes
AU - Antonino Flachi
AU - Marco Pasini
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2606.29307
UR - https://arxiv.org/abs/2606.29307
AB - A quantum macroscopic ``Kruskal'' black hole solution that incorporates quantum geometry effects has been derived in \chg{loop quantum gravity} as the counterpart to the classical Schwarzschild solution with a distinct imprint outside the event horizon, even at scales much larger than the Planck length. This resulting black hole quantum geometry is supported by an effective energy density of quantum origin, outside the horizon, which prevents asymptotic flatness at large distances and confines massive particles to finite radii, thereby preventing their escape to infinity. In this work\chg{,} we adapt to these solutions the extended Anderson-Candelas-Christensen-DeWitt approach to compute the quantum vacuum polarization in order to provide an accurate measure of the quantum activity around these black holes. We carry out a numerical implementation of the formalism and present, to our knowledge for the first time, the scalar vacuum polarization ⟨ϕ^2⟩ exterior to this quantum-corrected geometry. We find that the quantum-gravity exponent ε enhances the near-horizon polarization and induces, farther out, a small negative tail that we identify---through a parameter-free \chg{DeWitt-Schwinger} comparison---with the field's response to the nonzero curvature of the background (absent for Ricci-flat Schwarzschild). The correction scales linearly with ε, the parameter tracking the quantum gravitational corrections, so that\chg{,} for astrophysically realistic (i.e., tiny) ε, the result is numerically indistinguishable from Schwarzschild. The calculation furnishes a consistency check on the quantum activity around these solutions, the fluctuations tracking the local curvature without anomalous growth in the exterior.
ER -