How Universal Is the Black Hole Zeroth Law?
Abstract
The black hole zeroth law asserts the thermal equilibrium of a stationary Killing horizon, yet its status beyond general relativity remains limited. We demonstrate that its validity is not governed by a universal mechanism: distinct gravitational theories enforce constancy of the surface gravity through different horizon-projections of their field equations. In general relativity, f(R)-gravity, and Lovelock theories, the zeroth law is known to follow from the mixed (null-transverse) horizon equations. By contrast, we show that in non-Lovelock theories the zeroth law is enforced by qualitatively different mechanisms. In generalized quadratic gravity, for instance, the null-null component of the field equations dictates its validity. Exploiting this novel diagnostic, we obtain the first exact proof of the zeroth law in the broader landscape of higher-curvature gravity, without relying on a perturbative expansion around general relativity. Our result establishes the zeroth law as a sharp probe of the underlying thermodynamic structure of gravity, and points toward a classification of modified theories according to the mechanism responsible for its validity.
Related
- Universal framework for horizon-scale tests of gravity with black hole shadows
- Universal Bounds on Black Hole Observables Imposed by Energy Conditions
- Universal Structure of Horizon Formation in Generic Binary Black Hole Mergers
- Adiabatic Deformations of Black Hole Moduli: II. The Magnetic GHS Family
- Parameter Estimation for Eccentric Supermassive Black Hole Binaries with Pulsar Timing Arrays
BibTeX
@misc{ghosh2026universal,
title = {{How Universal Is the Black Hole Zeroth Law?}},
author = {Rajes Ghosh and Sudipta Sarkar},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24648},
eprint = {2609.24648},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24648},
}
RIS
TY - UNPB
TI - How Universal Is the Black Hole Zeroth Law?
AU - Rajes Ghosh
AU - Sudipta Sarkar
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24648
UR - https://arxiv.org/abs/2609.24648
AB - The black hole zeroth law asserts the thermal equilibrium of a stationary Killing horizon, yet its status beyond general relativity remains limited. We demonstrate that its validity is not governed by a universal mechanism: distinct gravitational theories enforce constancy of the surface gravity through different horizon-projections of their field equations. In general relativity, f(R)-gravity, and Lovelock theories, the zeroth law is known to follow from the mixed (null-transverse) horizon equations. By contrast, we show that in non-Lovelock theories the zeroth law is enforced by qualitatively different mechanisms. In generalized quadratic gravity, for instance, the null-null component of the field equations dictates its validity. Exploiting this novel diagnostic, we obtain the first exact proof of the zeroth law in the broader landscape of higher-curvature gravity, without relying on a perturbative expansion around general relativity. Our result establishes the zeroth law as a sharp probe of the underlying thermodynamic structure of gravity, and points toward a classification of modified theories according to the mechanism responsible for its validity.
ER -