Xu Mou, Zhang Yuying, Yang Liu, Yang Shining, Lu Jianbo
Department of Physics, Liaoning Normal University, Dalian 116029, China.
Entropy (Basel). 2024 Oct 15;26(10):868. doi: 10.3390/e26100868.
The thermodynamics of black holes (BHs) and their corrections have become a hot topic in the study of gravitational physics, with significant progress made in recent decades. In this paper, we study the thermodynamics and corrections of spherically symmetric BHs in models f(R)=R+αR2 and f(R)=R+2γR+8Λ under the f(R) theory, which includes the electrodynamic field and the cosmological constant. Considering thermal fluctuations around equilibrium states, we find that, for both f(R) models, the corrected entropy is meaningful in the case of a negative cosmological constant (anti-de Sitter-RN spacetime) with Λ=-1. It is shown that when the BHs' horizon radius is small, thermal fluctuations have a more significant effect on the corrected entropy. Using the corrected entropy, we derive expressions for the relevant corrected thermodynamic quantities (such as Helmholtz free energy, internal energy, Gibbs free energy, and specific heat) and calculate the effects of the correction terms. The results indicate that the corrections to Helmholtz free energy and Gibbs free energy, caused by thermal fluctuations, are remarkable for small BHs. In addition, we explore the stability of BHs using specific heat. The study reveals that the corrected BH thermodynamics exhibit locally stable for both models, and corrected systems undergo a Hawking-Page phase transition. Considering the requirement on the non-negative volume of BHs, we also investigate the constraint on the EH radius of BHs.
黑洞（BHs）的热力学及其修正已成为引力物理学研究中的一个热门话题，近几十年来取得了重大进展。在本文中，我们在包含电磁场和宇宙学常数的(f(R))理论下，研究(f(R)=R+\alpha R^2)和(f(R)=R + 2\gamma R + 8\Lambda)模型中球对称黑洞的热力学及其修正。考虑平衡态附近的热涨落，我们发现，对于这两种(f(R))模型，在宇宙学常数为负（反德西特 - RN时空）且(\Lambda = -1)的情况下，修正后的熵是有意义的。结果表明，当黑洞的视界半径较小时，热涨落对修正后的熵有更显著的影响。利用修正后的熵，我们推导了相关修正热力学量（如亥姆霍兹自由能、内能、吉布斯自由能和比热）的表达式，并计算了修正项的影响。结果表明，热涨落引起的对亥姆霍兹自由能和吉布斯自由能的修正，对于小黑洞来说是显著的。此外，我们利用比热来探讨黑洞的稳定性。研究表明，两种模型的修正黑洞热力学都表现出局部稳定性，且修正后的系统会经历霍金 - 佩奇相变。考虑到对黑洞非负体积的要求，我们还研究了对黑洞事件视界半径的约束。
