Calculating the Hawking Temperature of Black Holes in $f(Q)$ Gravity Using the RVB Method: A Residue-Based Approach

TL;DR

This paper introduces a residue-based method for calculating Hawking temperatures in $f(Q)$ gravity, revealing an additional correction term linked to contour integral residues, enhancing understanding of black hole thermodynamics in modified gravity.

Contribution

It presents a novel residue-based approach to compute Hawking temperatures in $f(Q)$ gravity, identifying a correction term from contour integral residues across various black hole models.

Findings

The correction term is consistently interpretable as a residue of a specific contour integral.

The method applies to multiple $f(Q)$ models including quadratic, logarithmic, and power law.

The approach offers new insights into black hole thermodynamics in modified gravity theories.

Abstract

This paper investigates the computation of Hawking temperatures for black holes within various $f(Q)$ gravity models using the RVB method. This topological approach uncovers an additional term in the temperature calculation, which we propose originates from the residue of a specific contour integral related to the metric or curvature. By examining several specific $f(Q)$ models including quadratic, logarithmic, square root, and power law modifications as well as well known black hole solutions such as RN, Kerr, and KN black holes, we demonstrate that the correction term can consistently be interpreted as this residue. Our findings provide new insights into black hole thermodynamics within modified gravity frameworks.