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