Quantum Love and ringdown near extremality
Abstract
In this paper we discuss the quasinormal modes and the tidal responses of a four-dimensional asymptotically flat Reissner-Nordström black hole near extremality and investigate the nontrivial near-horizon quantum corrections of these observables. The near-horizon dynamics of near extremal black holes are generally governed by an effective Schwarzian action coupled to boundary gauge modes. We use this description and couple this effective theory with a massless scalar field outside. Using this setup we compute 2 → 2 scattering process of a black hole and a scalar particle. The poles of the scattering amplitude at complex frequencies give us the quasinormal mode spectrum and we recover the predicted zero damped modes near extremality at leading order. Next we evaluate the static Love numbers from the elastic limit of the scattering amplitude. We show that the static Love numbers are non-zero in contrast to the classical expectations. Very close to extremality, the behaviour is analytic, but as the near-extremal energy becomes sufficiently large, we find logarithmic dependence on the energy. This cannot be removed by the choice of renormalisation scheme. Thus near-horizon quantum effects non-trivially change the tidal response of near-extremal black holes.
Related
- Love at First Loop: Quantum Deformability of Near-Extremal Black Holes
- Resumming Kerr Quasinormal-Mode Frequencies: Accuracy and Breakdown Near Extremality
- Collapse to extremality: The third law of black hole thermodynamics in quantum gravity
- Quantum black hole ringdown
- Quantum Love Numbers are Non-Zero
BibTeX
@misc{bhattacharjee2026quantum,
title = {{Quantum Love and ringdown near extremality}},
author = {Arindam Bhattacharjee and Muktajyoti Saha and M. V. S. Saketh},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03708},
eprint = {2610.03708},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03708},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum Love and ringdown near extremality
AU - Arindam Bhattacharjee
AU - Muktajyoti Saha
AU - M. V. S. Saketh
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.03708
UR - https://arxiv.org/abs/2610.03708
AB - In this paper we discuss the quasinormal modes and the tidal responses of a four-dimensional asymptotically flat Reissner-Nordström black hole near extremality and investigate the nontrivial near-horizon quantum corrections of these observables. The near-horizon dynamics of near extremal black holes are generally governed by an effective Schwarzian action coupled to boundary gauge modes. We use this description and couple this effective theory with a massless scalar field outside. Using this setup we compute 2 → 2 scattering process of a black hole and a scalar particle. The poles of the scattering amplitude at complex frequencies give us the quasinormal mode spectrum and we recover the predicted zero damped modes near extremality at leading order. Next we evaluate the static Love numbers from the elastic limit of the scattering amplitude. We show that the static Love numbers are non-zero in contrast to the classical expectations. Very close to extremality, the behaviour is analytic, but as the near-extremal energy becomes sufficiently large, we find logarithmic dependence on the energy. This cannot be removed by the choice of renormalisation scheme. Thus near-horizon quantum effects non-trivially change the tidal response of near-extremal black holes.
ER -