Document Type : Regular article

Author

• Sameer Ahmad Mir

Department of Physics, Jamia Millia Islamia, New Delhi, 110025, India.

Abstract

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 $b$.

Keywords

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

Main Subjects

• Physics