Understanding gravitational entropy of black holes: A new proposal via curvature invariants

Partly motivated by the arrow of time problem in cosmology and Weyl curvature hypothesis formulated Roger Penrose, previous works literature have proposed---among other possibilities---the square as being underlying entropy density function black hole entropy, but proposal suffers from a few drawbacks. In this work, we propose new also based solely on curvature, adopting some combinations invariants. As an improvement find that our method for all static solutions four- five-dimensional general relativity regardless whether they are empty space or not. It should be possible to generalize higher dimensions. This allows us discuss physical interpretation which remains somewhat mysterious. Extending modified theories gravity, work suggests gravitational is manifestation different effects since need choose quantities.