From thermodynamics to the solutions in gravity theory

In a recent work, we present a new point of view to the relation of gravity and thermodynamics, in which we derive the Schwarzschild solution through thermodynamic considerations by the aid of the Misner-Sharp mass in an adiabatic system. In this Letter 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 Gauss-Bonnet gravity. Using this gravi-thermodynamic thought, we obtain a NEW class of solution in F(R) gravity in an n-dimensional (n >= 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. (C) 2014 Published by Elsevier B.V.