Quantum Love Numbers are Non-Zero
Abstract
The static Love numbers of four-dimensional Schwarzschild black holes vanish classically. We show that this is not true in the quantum theory. Working in the worldline effective field theory, we compute the leading quantum correction to the Compton amplitude for massless scalars and photons scattering off a Schwarzschild black hole at first post-Minkowskian order, and find logarithmic divergences associated with the renormalization of the static Love numbers. We conclude that renormalization-group running necessarily generates Love numbers suppressed by the square of the Planck length in units of the horizon radius, ℓpl2/rh2. This is consistent with the classical vanishing being a consequence of an accidental symmetry of static general relativity, broken by quantum loops. Extrapolated to gravitational perturbations, our results suggest that the quadrupolar static Love numbers of Schwarzschild are of size λ∼ M rh2 ℓpl2.
Related
BibTeX
@misc{elkhidir2026quantum,
title = {{Quantum Love Numbers are Non-Zero}},
author = {Asaad Elkhidir and Godwin Martin and Julio Parra-Martinez and M.V.S Saketh},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25875},
eprint = {2609.25875},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05781720v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum Love Numbers are Non-Zero
AU - Asaad Elkhidir
AU - Godwin Martin
AU - Julio Parra-Martinez
AU - M.V.S Saketh
PY - 2026
DA - 2026/09/22
PB - HAL
DO - 10.48550/arxiv.2609.25875
UR - https://hal.science/hal-05781720v1
AB - The static Love numbers of four-dimensional Schwarzschild black holes vanish classically. We show that this is not true in the quantum theory. Working in the worldline effective field theory, we compute the leading quantum correction to the Compton amplitude for massless scalars and photons scattering off a Schwarzschild black hole at first post-Minkowskian order, and find logarithmic divergences associated with the renormalization of the static Love numbers. We conclude that renormalization-group running necessarily generates Love numbers suppressed by the square of the Planck length in units of the horizon radius, ℓ_pl^2/r_h^2. This is consistent with the classical vanishing being a consequence of an accidental symmetry of static general relativity, broken by quantum loops. Extrapolated to gravitational perturbations, our results suggest that the quadrupolar static Love numbers of Schwarzschild are of size λ∼ M r_h^2 ℓ_pl^2.
ER -