Abstract
We investigate the stability criterions for perfect fluid in f(R) theories which is an important generalization of general relativity. Firstly, using Wald’s general variation principle, we recast Seifert’s work and obtain the dynamical stability criterion. Then using our generalized thermodynamical criterion, we obtain the concrete expressions of the criterion. We show that the dynamical stability criterion is exactly the same as the thermodynamical stability criterion to spherically symmetric perturbations of static spherically symmetric background solutions. This result suggests that there is an inherent connection between the thermodynamics and gravity in f(R) theories. It should be pointed out that using the thermodynamical method to determine the stability for perfect fluid is simpler and more directly than the dynamical method.
Highlights
It is well-known that using the first variation of gravitational equation one can obtain the dynamical stability criterion
A system is thermodynamical stable means that the system is in the thermodynamical equilibrium and the second variation of the total entropy of the system is negative, δ2 S < 0
In Ref. [24], we presented a generalized thermodynamical criterion, which is the second variation of total entropy for perfect fluid star
Summary
It is well-known that using the first variation of gravitational equation one can obtain the dynamical stability criterion Chandrasekhar first discussed this problem and got the stability criterion for perfect fluid in general relativity [11]. [24], we presented a generalized thermodynamical criterion, which is the second variation of total entropy for perfect fluid star. As an important generalization of general relativity, f (R) theories can explain the accelerated expansion of the universe because it contains higher order invariants in the action [25,26] In this manuscript, we show that the dynamical stability criterion is the same as the thermodynamical stability criterion in f (R) theories, which implies that there is an inherent connection between thermodynamics and gravity. [18] can not directly degenerate to general relativity, we recast the process of how to obtain the stability criterion by dynamical method.
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