Black Hole Entropy in f(Q) Gravity from the RVB Residue Method

TL;DR

This paper develops a residue-based method to calculate black hole entropy in f(Q) gravity, revealing corrections to the Bekenstein-Hawking law due to residue contributions.

Contribution

It extends the RVB residue method from temperature to entropy calculation in f(Q) gravity, providing a universal integral relation and explicit formulas for specific models.

Findings

Derived a general entropy expression incorporating residue effects.

Recovered the Bekenstein-Hawking law when residue effects vanish.

Found that residue contributions lead to entropy corrections beyond the area law.

Abstract

We extend the residue-based Robson-Villari-Biancalana (RVB) method from the calculation of Hawking temperature to the determination of black hole entropy within f(Q) gravity. Starting from the residue-corrected temperature prescription developed in recent RVB analyses of f(Q) black holes, we combine this approach with the first law of black hole thermodynamics to derive a general expression for the entropy of static, spherically symmetric configurations. By expressing the metric in a standard Schwarzschild-like decomposition with an additional correction term, we show that the entropy satisfies a universal integral relation. The integrand depends explicitly on horizon data as well as on a residue-induced temperature shift parameter. For the specific quadratic model, we obtain an explicit closed-form expression for the entropy at first order in the residue parameter. In the limit where the residue contribution vanishes, the standard Bekenstein-Hawking area law is recovered. However, once the complex contour contribution is retained, a correction beyond the area law naturally emerges. This framework should be interpreted as a residue-induced thermodynamic extension of the temperature-based method, rather than as a universal Noether charge formulation applicable to all f(Q) black hole solutions.