General proof of the entropy principle for self-gravitating fluid in f (R) gravity

Abstract

The discussions on the connection between gravity and thermodynamics attract much attention recently. We consider a static self-gravitating perfect fluid system in f (R) gravity, which is an important theory could explain the accelerated expansion of the universe. We first show that the Tolman-Oppenheimer-Volkoff equation of f (R) theories can be obtained by thermodynamical method in spherical symmetric spacetime. Then we prove that the maximum entropy principle is also valid for f (R) gravity in general static spacetimes beyond spherical symmetry. The result shows that if the constraint equation is satisfied and the temperature of fluid obeys Tolmans law, the extrema of total entropy implies other components of gravitational equations. Conversely, if f (R) gravitational equation hold, the total entropy of the fluid should be extremum. Our work suggests a general and solid connection between f (R) gravity and thermodynamics.

Consistency between dynamical and thermodynamical stabilities for perfect fluid in f(R) theories

“…It is worthy noting that P 3↔4 Dyn should be considered when we obtain the coefficient C 8 Dyn of bξ term in subsequent calculation. We also have…”

“…Verlinder suggested that the gravity is the entropy force [3]. In recent years, the proofs of the maximum entropy principle showed that the gravitational equation can be derived from the constraint equation and the maximum of total entropy [5][6][7][8][9][10]. All these researches are trying to establish a correspona e-mail: fangxj@hunnu.edu.cn b e-mail: hexiaokai77@163.com c e-mail: jljing@hunn.edu.cn dence between the first variation of thermodynamic quantities and gravitational equation.…”

Thermodynamical stability for a perfect fluid

“…Meanwhile, a series of papers proved that the maximum entropy principle for a perfect fluid holds in different theories. This principle shows that if the constraint equation and some thermodynamic conditions are satisfied, the gravitational field equations could be derived by the extrema of the total entropy [3][4][5][6][7][8][9]. Recently, Jacobson proposed the "causal diamond" structure and considered entanglement equilibrium to imply the Einstein equations [10].…”

Consistency between dynamical and thermodynamical stabilities for charged self-gravitating perfect fluid

“…In recent years, the proof of the maximum entropy principle have shown that, for self-gravitating perfect fluid, the gravitational equation can be derived from the constraint equation and the thermodynamic relation [3][4][5][6][7]. It has been proved that this principle not only applicable to general relativity, but also to other modified gravity theories, such as Lovelock gravity and f (R) theories [8,9].…”