Kasner Exponents from the Bouncing Singularity
Abstract
Thermal two-point functions of holographic CFTs can probe the black hole singularity. When a bouncing geodesic exists, the correlator at leading order in 1/N develops a singularity G(t, x⃗=0) ∝ (tc−t)−2Δ+bt, where Δ is the scaling dimension of the operator. We show that the additional exponent bt is determined by the Kasner exponents near the singularity. From the wave reflected off the singularity, which gives an exponentially small term in the large-frequency retarded correlator, we derive the formula bt=(d−1) max ( (pi−pt)/(1−pt), 1/2 ) for planar black branes in AdSd+1, where pt and pi are the Kasner exponents of the time and spatial directions. We compare our formula with the numerical values of Čeplak and Valach. It reproduces the relation that they proposed for a special class of black branes. For more general black branes, where no formula had been found, our formula agrees with most of their numerical data and fits them much better than the extension of their relation. We also give predictions for bt in theories where the Kasner exponents are known, but bt has not been computed.
Related
BibTeX
@misc{oh2026kasner,
title = {{Kasner Exponents from the Bouncing Singularity}},
author = {Hyunwoo Oh},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31699},
eprint = {2610.31699},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31699},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Kasner Exponents from the Bouncing Singularity
AU - Hyunwoo Oh
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.31699
UR - https://arxiv.org/abs/2610.31699
AB - Thermal two-point functions of holographic CFTs can probe the black hole singularity. When a bouncing geodesic exists, the correlator at leading order in 1/N develops a singularity G(t, x⃗=0) ∝ (t_c−t)^−2Δ+b_t, where Δ is the scaling dimension of the operator. We show that the additional exponent b_t is determined by the Kasner exponents near the singularity. From the wave reflected off the singularity, which gives an exponentially small term in the large-frequency retarded correlator, we derive the formula b_t=(d−1) max ( (p_i−p_t)/(1−p_t), 1/2 ) for planar black branes in AdS_d+1, where p_t and p_i are the Kasner exponents of the time and spatial directions. We compare our formula with the numerical values of Čeplak and Valach. It reproduces the relation that they proposed for a special class of black branes. For more general black branes, where no formula had been found, our formula agrees with most of their numerical data and fits them much better than the extension of their relation. We also give predictions for b_t in theories where the Kasner exponents are known, but b_t has not been computed.
ER -