Inner Horizon Saddles and a Spectral KSW Criterion
Abstract
The Bekenstein-Hawking entropy formula ρ= eA/4G receives significant corrections for charged black holes near extremality. Using standard results in JT gravity, the correction term can semiclassically be expressed as minus the exponential of the inner horizon area, eAinner/4G, and the cancellation between these two exponentials enforces a vanishing density of states towards extremality, when the two horizons collide. Building on arXiv:2402.10162, we argue that the correction term corresponds to a complex saddle geometry of the bulk gravitational path integral. The proposed geometry has a negative boundary length and caps off at the inner horizon; we refer to it as the inner horizon saddle. We discuss how the saddle, and its accompanying minus sign, contribute to the density of states through a Picard-Lefschetz analysis of the inverse Laplace contour, together with a stability analysis of the saddle. We also address the inner horizon saddle's violation of the Kontsevich-Segal-Witten (KSW) allowability criterion for the inclusion of complex metrics. Despite this violation, which is believed to cause unphysical divergences in path integral computations, one can describe one-loop effects on the inner horizon saddle by carefully treating wrong-sign modes. Motivated by this observation, we propose a weaker version of the KSW criterion, which we call the spectral KSW criterion. Its purpose is to characterize when one-loop corrections around complex gravitational saddles are well defined.
Related
- Single-horizon regular black holes and the fate of the inner-horizon instability
- At Most One Inner Killing Horizon in Stationary Black Holes
- Global curvature control in a regular black hole with Minkowski core and inner-extremal horizon
- Global curvature control in a regular black hole with Minkowski core and inner-extremal horizon
- Black-Hole First Laws and Horizon Constraints: A Differential Rank Criterion
BibTeX
@misc{caminiti2026inner,
title = {{Inner Horizon Saddles and a Spectral KSW Criterion}},
author = {Jacqueline Caminiti and Aidan Herderschee},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.08335},
eprint = {2605.08335},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.08335},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Inner Horizon Saddles and a Spectral KSW Criterion
AU - Jacqueline Caminiti
AU - Aidan Herderschee
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2605.08335
UR - https://arxiv.org/abs/2605.08335
AB - The Bekenstein-Hawking entropy formula ρ= e^A/4G receives significant corrections for charged black holes near extremality. Using standard results in JT gravity, the correction term can semiclassically be expressed as minus the exponential of the inner horizon area, e^A_inner/4G, and the cancellation between these two exponentials enforces a vanishing density of states towards extremality, when the two horizons collide. Building on arXiv:2402.10162, we argue that the correction term corresponds to a complex saddle geometry of the bulk gravitational path integral. The proposed geometry has a negative boundary length and caps off at the inner horizon; we refer to it as the inner horizon saddle. We discuss how the saddle, and its accompanying minus sign, contribute to the density of states through a Picard-Lefschetz analysis of the inverse Laplace contour, together with a stability analysis of the saddle. We also address the inner horizon saddle's violation of the Kontsevich-Segal-Witten (KSW) allowability criterion for the inclusion of complex metrics. Despite this violation, which is believed to cause unphysical divergences in path integral computations, one can describe one-loop effects on the inner horizon saddle by carefully treating wrong-sign modes. Motivated by this observation, we propose a weaker version of the KSW criterion, which we call the spectral KSW criterion. Its purpose is to characterize when one-loop corrections around complex gravitational saddles are well defined.
ER -