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

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. 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.

18pages

References in corpus (8)

• Entanglement Equilibrium and the Einstein Equation
• Stability of spherically symmetric solutions in modified theories of gravity
• A general variational principle for spherically symmetric perturbations in diffeomorphism covariant theories
• Maximum Entropy Principle for Self-gravitating Perfect Fluid in Lovelock Gravity
• Proof of entropy principle in Einstein-Maxwell theory
• Thermodynamical stability for perfect fluid
• General proof of (maximum) entropy principle in Lovelock gravity
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Cited by in corpus (4)

• Thermal stability of a special class of black hole solutions in F(R) gravity
• Dynamic and Thermodynamic Stability of Charged Perfect Fluid Stars
• Consistency between dynamical and thermodynamical stabilities for charged self-gravitating perfect fluid
• Universality of entropy principle for a general diffeomorphism-covariant purely gravitational theory