https://doi.org/10.1140/epjc/s10052-018-6053-0
Regular Article - Theoretical Physics
Consistency between dynamical and thermodynamical stabilities for perfect fluid in f(R) theories
1
Department of Physics, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha, 410081, Hunan, People’s Republic of China
2
School of Mathematics and Computational Science, Hunan First Normal University, Changsha, 410205, People’s Republic of China
* e-mail: jljing@hunn.edu.cn
Received:
5
June
2017
Accepted:
8
July
2018
Published online:
4
August
2018
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.
© The Author(s), 2018
