General proof of the entropy principle for self-gravitating fluid in f(R) Gravity

Understand

The discussions on the connection between gravity and thermodynamics attract much attention recently.

• We consider a static self-gravitating perfect fluid system in $f(R)$ gravity, which is an important theory could explain the accelerated expansion of the universe.
• We first show that the Tolman-Oppenheimer-Volkoff equation of $f(R)$ theories can be obtained by thermodynamical method in spherical symmetric spacetime.
• Then we prove that the maximum entropy principle is also valid for $f(R)$ gravity in general static spacetimes beyond spherical symmetry.