Can One Hear the Absence of a Singularity?
Abstract
One of the central expectations of quantum gravity is the resolution of the curvature singularities predicted by General Relativity, potentially giving rise to effective black-hole geometries that are regular inside the horizon. We show that, for a very broad class of regular black holes including several known solutions, the quasinormal-mode spectrum in the large-overtone limit differs discontinuously from that of a Schwarzschild black hole, even when the regularization parameter is arbitrarily small. The real part of the quasinormal frequencies vanishes asymptotically, rather than approaching a nonzero constant, as generically occurs in General Relativity and other theories predicting black holes with curvature singularities. The asymptotic black-hole spectrum thus retains a distinctive imprint of singularity resolution. We establish these results analytically through a systematic formulation of the monodromy method and confirm them numerically. We interpret this phenomenon as a manifestation of black-hole spectral instability, whereby arbitrarily small deviations from vacuum General Relativity produce nonperturbative changes in the large-overtone spectrum.
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BibTeX
@misc{rocca2026hear,
title = {{Can One Hear the Absence of a Singularity?}},
author = {Matteo Della Rocca and Paolo Pani and Andrea P. Sanna},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37028},
eprint = {2610.37028},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37028},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Can One Hear the Absence of a Singularity?
AU - Matteo Della Rocca
AU - Paolo Pani
AU - Andrea P. Sanna
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37028
UR - https://arxiv.org/abs/2610.37028
AB - One of the central expectations of quantum gravity is the resolution of the curvature singularities predicted by General Relativity, potentially giving rise to effective black-hole geometries that are regular inside the horizon. We show that, for a very broad class of regular black holes including several known solutions, the quasinormal-mode spectrum in the large-overtone limit differs discontinuously from that of a Schwarzschild black hole, even when the regularization parameter is arbitrarily small. The real part of the quasinormal frequencies vanishes asymptotically, rather than approaching a nonzero constant, as generically occurs in General Relativity and other theories predicting black holes with curvature singularities. The asymptotic black-hole spectrum thus retains a distinctive imprint of singularity resolution. We establish these results analytically through a systematic formulation of the monodromy method and confirm them numerically. We interpret this phenomenon as a manifestation of black-hole spectral instability, whereby arbitrarily small deviations from vacuum General Relativity produce nonperturbative changes in the large-overtone spectrum.
ER -