Thermodynamic geometric analysis of RN black holes under f(R) gravity

Abstract

In this article, we explore the RN black hole under f(R) gravity and its thermodynamic properties. We begin by examining the small fluctuations around the equilibrium state and summarizing the expression for the modified thermodynamic entropy of this black hole. Additionally, we delve into the geometric thermodynamics (GTD) of black holes and investigate the suitability of the curvature scalar of the GTD method for the phase transition point of the black hole. Moreover, we investigate the effects of modified parameters on the thermodynamic behavior of black holes.Within the framework of $f(R)$ modified gravity theory, we discovered that several RN black holes demonstrate thermodynamic properties resembling those of an ideal gas when the initial curvature scalar of the black hole remains constant. However, if the initial curvature scalar is non-constant and the cosmological constant term possesses a negative exponent, the Reissner-Nordström (RN) black holes could exhibit characteristics akin to those of a van der Waals gas.We separately list the general solutions for the case of non-negative powers and the special solutions for the case of negative powers. We observe that, under certain conditions, the phase transition analogous to the Van der Waals gas exists for charged black holes under f(R) gravity.

arXiv commentThis work is partially supported by the National Natural Science Foundation of China(No. 11873025).We would like to thank Zhan-Feng Mai at Peking University for his generous help. arXiv admin note: substantial text overlap with arXiv:2312.10043

References in corpus (24)

• Is Cosmic Speed-Up Due to New Gravitational Physics?
• P-V criticality of charged AdS black holes
• Conditions for the cosmological viability of f(R) dark energy models
• Curvature quintessence matched with observational data
• General Logarithmic Corrections to Black Hole Entropy
• Spherically symmetric solutions of modified field equations in f(R) theories of gravity
• Insight into the Microscopic Structure of an AdS Black Hole from Thermodynamical Phase Transition
• The Cosmology of f(R) Gravity in the Metric Variational Approach
• Moduli, Scalar Charges, and the First Law of Black Hole Thermodynamics
• Repulsive Interactions and Universal Properties of Charged Anti-de Sitter Black Hole Microstructures
• Static Spherically Symmetric Solutions in F(R) Gravity
• f(R) Black holes
• Some exact solutions of F(R) gravity with charged (a)dS black hole interpretation
• Viable Singularity-Free f(R) Gravity Without a Cosmological Constant
• Fake Supersymmetry and Extremal Black Holes
• Hawking-Page phase transition in BTZ black hole revisited
• Holographic actions from black hole entropy
• Thermodynamic geometry of black holes in f(R) gravity
• Dynamic properties of thermodynamic phase transition for five-dimensional neutral Gauss-Bonnet AdS black hole on free energy landscape
• Generation of spherically symmetric metrics in $f\left(R\right)$ gravity
• Hawking-Page Phase Transition of black Dp-branes and R-charged black holes with an IR Cutoff
• Thermodynamics and gauge/gravity duality for Lifshitz black holes in the presence of exponential electrodynamics
• The effects of massive graviton on the equilibrium between the black hole and radiation gas in an isolated box
• Calculating the Hawking Temperatures of Conventional Black Holes in the f(R) Gravity Models with the RVB Method