Bounds on the minimum orbital period of general static spherical black holes: a sharp upper bound and a conditional lower bound
Abstract
We investigate bounds on the minimum orbital period around four-dimensional general static spherical black holes. For all static spherically symmetric black holes with an event horizon, asymptotic flatness and non-negative energy density outside the horizon, we prove Tmin≤ 6√3 πM. The bound is sharp and is saturated by the Schwarzschild solution. The lower bound requires an additional condition on the exterior matter: under the tangential pressure condition pτ≥(κ/2)ρ with κ>1, imposed for all r≥ rg, where rg is the largest radius at which T(r) attains its global minimum, we prove Tmin≥ c(κ)M with c(κ)=6√3π(κ−1)√(κ+2)/κ3/2. In summary, both bounds apply to the same geometric class and differ only in what they demand of the matter: non-negative energy density suffices for the upper bound, while the lower bound is established under the additional tangential pressure condition.
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BibTeX
@misc{peng2026bounds,
title = {{Bounds on the minimum orbital period of general static spherical black holes: a sharp upper bound and a conditional lower bound}},
author = {Yan Peng and Guohua Liu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40843},
eprint = {2610.40843},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40843},
}
RIS
TY - UNPB
TI - Bounds on the minimum orbital period of general static spherical black holes: a sharp upper bound and a conditional lower bound
AU - Yan Peng
AU - Guohua Liu
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40843
UR - https://arxiv.org/abs/2610.40843
AB - We investigate bounds on the minimum orbital period around four-dimensional general static spherical black holes. For all static spherically symmetric black holes with an event horizon, asymptotic flatness and non-negative energy density outside the horizon, we prove T_min≤ 6√3 πM. The bound is sharp and is saturated by the Schwarzschild solution. The lower bound requires an additional condition on the exterior matter: under the tangential pressure condition p_τ≥(κ/2)ρ with κ>1, imposed for all r≥ r_g, where r_g is the largest radius at which T(r) attains its global minimum, we prove T_min≥ c(κ)M with c(κ)=6√3π(κ−1)√(κ+2)/κ^3/2. In summary, both bounds apply to the same geometric class and differ only in what they demand of the matter: non-negative energy density suffices for the upper bound, while the lower bound is established under the additional tangential pressure condition.
ER -