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arXiv · 2508.05326

A universal relation among Euclidean integrals for black holes in higher-derivative gravity theories

Yong Xiao·Qiang Wang·Aonan Zhang
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Abstract

In this paper, we establish a universal equality governing Euclidean integrals of gravitational actions in higher-derivative theories. This relation is shown to hold universally for asymptotically flat black holes in pure gravity, and is generalized to asymptotically anti-de Sitter (AdS) spacetimes through appropriate regularization. We further examine its validity in systems with matter-gravity coupling, identifying that violations occur only when matter fields exhibit pathological behaviors: divergence at the horizon or non-decaying profiles at infinity. These findings reveal fundamental constraints on gravitational thermodynamics and provide diagnostic tools for identifying ill-behaved matter configurations.

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Yong Xiao, Qiang Wang, Aonan Zhang. 2025-08-07. A universal relation among Euclidean integrals for black holes in higher-derivative gravity theories. https://doi.org/10.1103/njlp-rm1c

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