Matter Induced Bounds: Photon Ring, Lyapunov Exponent, Induced Temperature
Abstract
We investigate analytic bounds on the equatorial photon ring radius and the Lyapunov exponent in rotating black holes containing anisotropic matter. For a constant equatorial equation-of-state parameter, the finite asymptotic mass and nonnegative energy density imply an upper bound on the photon ring radius given by the Kerr photon ring radius with the same asymptotic mass and rotation parameters for co-rotating and counter-rotating motions. The lower bounds are written in terms of the quantities evaluated at the outer horizon. These bounds on the Lyapunov exponent constrain the absolute magnitude of the imaginary part of the quasinormal frequency of a massless scalar field within the eikonal limit. The worldsheet surface gravity and induced temperature were derived for a probe string in the Penrose limit along the photon ring. The induced temperature and worldsheet surface gravity give an upper bound on the photon ring Lyapunov exponent, 2 πTind = κind ≥ λ.
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BibTeX
@misc{lee2026matter,
title = {{Matter Induced Bounds: Photon Ring, Lyapunov Exponent, Induced Temperature}},
author = {Hocheol Lee and Bogeun Gwak},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30736},
eprint = {2610.30736},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30736},
}
RIS
TY - UNPB
TI - Matter Induced Bounds: Photon Ring, Lyapunov Exponent, Induced Temperature
AU - Hocheol Lee
AU - Bogeun Gwak
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.30736
UR - https://arxiv.org/abs/2610.30736
AB - We investigate analytic bounds on the equatorial photon ring radius and the Lyapunov exponent in rotating black holes containing anisotropic matter. For a constant equatorial equation-of-state parameter, the finite asymptotic mass and nonnegative energy density imply an upper bound on the photon ring radius given by the Kerr photon ring radius with the same asymptotic mass and rotation parameters for co-rotating and counter-rotating motions. The lower bounds are written in terms of the quantities evaluated at the outer horizon. These bounds on the Lyapunov exponent constrain the absolute magnitude of the imaginary part of the quasinormal frequency of a massless scalar field within the eikonal limit. The worldsheet surface gravity and induced temperature were derived for a probe string in the Penrose limit along the photon ring. The induced temperature and worldsheet surface gravity give an upper bound on the photon ring Lyapunov exponent, 2 πT_ind = κ_ind ≥ λ.
ER -