Phys.Rev.D, 112, 084030 (2025)
Black hole entropy bounded by the specific heat
Kai-Peng Lu1 and Hong Lu1,2
1 Center for Joint Quantum Studies, Department of Physics, School of Science, Tianjin University, Tianjin 300350, China.
2 Joint School of National University of Singapore and Tianjin University, International Campus of Tianjin University, Binhai New City, Fuzhou 350207, China.
* kaipenglu@tju.edu.cn, mrhonglu@gmail.com
Abstract
We propose new bounds on black hole entropy in terms of the specific heat at fixed charges. For special spherically symmetric and static black holes (gttgrr ¼ −1), we prove the bounds with suitable sufficient energy conditions. For more general static and rotating black holes, we test the bounds with a variety of examples. This work extends the previously known algebraic inequalities of the black hole thermodynamic variables such as the Penrose inequality, to include their derivatives.
