Hawking-Page Transition from Logarithmic Entropy in f(R) Gravity

We analyze the thermodynamics and phase structure of a static, spherically symmetric black hole that extends Schwarzschild within f(R) gravity. In the extended framework, we include a model-independent, one-loop-motivated logarithmic entropy correction with a free coefficient b. We derive closed-form expressions for temperature, enthalpy, corrected entropy, Gibbs free energy, and heat capacity to first order in the deformation parameter, and chart the Hawking-Page transition and local stability. A positive b suppresses local stability for small black holes, while negative b enhances it. We also state the generalized first law with the f(R) coupling as a thermodynamic variable, providing a practical phenomenology for future microscopic determinations of b.

کلیدواژه ها:

Black-hole thermodynamics ، Gibbs free energy ، Logarithmic entropy correction ، AdS black holes ، Phase structure and criticality ، Holographic implications