Calculating the Hawking temperature of black holes in <i>f</i>(<i>Q</i>) gravity using the RVB method: a residue-based approach

This paper explores the computation of Hawking temperatures for black holes within various f( Q) gravity models using the RVB (Robson–Villari–Biancalana) method. This topological approach reveals an additional term in the temperature calculation, which we propose is a residue arising from the contour integral [Formula: see text], where f( z) represents a function related to the black hole’s metric or curvature. By analyzing several specific f( Q) models including f( Q) = Q + α Q 2 , f( Q) = Q + βln ( Q), [Formula: see text], f( Q) = Q n as well as the Reissner–Nordstrm, Kerr, and Kerr–Newman black holes, we demonstrate that the correction term C can be consistently interpreted as this residue, providing new insights into black hole thermodynamics in modified gravity frameworks. We also expand on important physical aspects such as black hole stability, late-stage evaporation, extremality bounds in charged and rotating spacetimes, and potential novel phases emerging from different forms of f( Q).