Gravitational entropy of a Schwarzschild-type black hole

In this study, Clifton, Ellis and Tavakol’s gravitational entropy proposal is used to determine the entropy of free gravitational fields due to a spherical symmetric Schwarzschild-type black hole which is considered in the framework of f(R) gravity. In order to obtain the gravitational entropy, we calculate the Weyl tensor of the black hole to determine the Bel-Robinson tensor, giving the super energy density. By using the super energy density, we obtain the gravitational energy density and the gravitational temperature to calculate the gravitational entropy of the f(R) gravity black hole. This proposal can reproduce the Bekenstein-Hawking value in general relativity limit, but cannot reproduce it in the f(R) gravity case.