Conformal boundaries and the photon sphere of AdS black holes
Abstract
We study linearized gravitational perturbations of four-dimensional Schwarzschild-AdS black holes with finite timelike boundaries subject to conformal boundary conditions. These fix the conformal class of the induced metric and the mean curvature, while allowing the boundary Weyl mode to fluctuate. The photon sphere plays a distinguished role in this problem: a static boundary at this radius is totally umbilic, and the scalar problem separates exactly into independent bulk and boundary sectors. We prove the absence of exponentially growing scalar and vector modes for spherical harmonics of degree two and higher. We determine how large angular momentum instabilities are suppressed as the boundary approaches umbilicity. Near the horizon, we recover the universal Rindler spectrum, including sound and shear excitations. We numerically follow these fluid modes as the boundary is moved outwards and find that they approach standard gravitational quasinormal modes at the asymptotic AdS4 boundary. For large black holes, these asymptotic endpoints correspond to the sound and shear poles of the dual three-dimensional conformal field theory. We also study perturbations of the AdS4 black brane, where we find an analogous continuation of the fluid modes in the absence of an intermediate umbilic boundary.
Related
- Quasinormal modes of massive scalar perturbations in slow-rotation bumblebee black holes with traceless conformal electrodynamics
- Photon sphere for a dyonic black hole corresponding to A2 Toda chain
- Photon rings and shadows of black holes with non-minimal couplings between curvature and electromagnetic field
- Coherent quantum state corrections in RN–black holes: Photon dynamics, shadow casts, and energy backreaction
- Black-Hole Ringdown from Photon-Sphere Modes in an Elastic Analogue
BibTeX
@misc{arias2026conformal,
title = {{Conformal boundaries and the photon sphere of AdS black holes}},
author = {Raúl Arias and Valentino Di Pierro and Silvia Georgescu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40778},
eprint = {2610.40778},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40778},
}
RIS
TY - UNPB
TI - Conformal boundaries and the photon sphere of AdS black holes
AU - Raúl Arias
AU - Valentino Di Pierro
AU - Silvia Georgescu
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40778
UR - https://arxiv.org/abs/2610.40778
AB - We study linearized gravitational perturbations of four-dimensional Schwarzschild-AdS black holes with finite timelike boundaries subject to conformal boundary conditions. These fix the conformal class of the induced metric and the mean curvature, while allowing the boundary Weyl mode to fluctuate. The photon sphere plays a distinguished role in this problem: a static boundary at this radius is totally umbilic, and the scalar problem separates exactly into independent bulk and boundary sectors. We prove the absence of exponentially growing scalar and vector modes for spherical harmonics of degree two and higher. We determine how large angular momentum instabilities are suppressed as the boundary approaches umbilicity. Near the horizon, we recover the universal Rindler spectrum, including sound and shear excitations. We numerically follow these fluid modes as the boundary is moved outwards and find that they approach standard gravitational quasinormal modes at the asymptotic AdS_4 boundary. For large black holes, these asymptotic endpoints correspond to the sound and shear poles of the dual three-dimensional conformal field theory. We also study perturbations of the AdS_4 black brane, where we find an analogous continuation of the fluid modes in the absence of an intermediate umbilic boundary.
ER -