From thermodynamics to the solutions in gravity theory

Abstract

In a recent work, we present a new point of view to the relation of gravity and thermodynamics, in which we derive the \sch~solution through thermodynamic laws by the aid of the Misner-Sharp mass in an adiabatic system. In this paper we continue to investigate the relation between gravity and thermodynamics for obtaining solutions via thermodynamics. We generalize our studies on gravi-thermodynamics in Einstein gravity to modified gravity theories. By using the first law with the assumption that the Misner-Sharp mass is the mass for an adiabatic system, we reproduce the Boulware-Deser-Cai solution in Guass-Bonnet gravity. Using this gravi-thermodynamics thought, we obtain a NEW class of solution in $F(R)$ gravity in an $n$-dimensional (n$\ge$3) spacetime which permits three-type $(n-2)$-dimensional maximally symmetric subspace, as an extension of our recent three-dimensional black hole solution, and four-dimensional Clifton-Barrow solution in $F(R)$ gravity.

9pages

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Cited by in corpus (6)

• Black holes and gravitational waves in three-dimensional f(R) gravity
• Quasinormal Modes for Dynamical Black Holes
• Naked singularity, firewall, and Hawking radiation
• Dynamical spacetimes in conformal gravity
• Towards a sound massive cosmology
• Quasilocal Smarr relations for static black holes