Quantum-corrected thermodynamics of Schwarzschild AdS black holes in conformal Killing gravity

Abstract

We study Schwarzschild--AdS black holes in conformal Killing gravity with non-perturbative entropy corrections within the extended phase-space formalism. By deriving the quantum-corrected heat capacity, Helmholtz free energy, internal energy, and Gibbs free energy, we show that quantum corrections modify phase transition points and thermal stability mainly at small horizon radii, while classical behavior is recovered for large black holes. Critical behavior of van der Waals type appears exclusively for positive values of the conformal Killing parameter $a$. Applying the island prescription, we find that the entanglement entropy of Hawking radiation saturates after the Page time at $S_{\text{sat}} = 2(πr_H^2 + ηe^{-πr_H^2})$, thereby restoring unitarity. Stronger quantum corrections increase the entropy threshold and delay information recovery. Furthermore, we examine the universal thermodynamic relation in the extremal limit under a minimal perturbation of the AdS curvature radius. We prove that the quantum correction parameter $η$ cancels out completely, yielding the robust universal combination $U = -r_{\text{ext}}^3 / l^3$. This demonstrates that the universal relation remains stable against non-perturbative quantum corrections to the entropy.