  Classical invariants of General Relativity can be used to approximate the
entropy of the gravitational field. In this work, we study two proposed
estimators based on scalars constructed out from the Weyl tensor, in Kerr
spacetime. In order to evaluate Clifton, Ellis and Tavakol's proposal, we
calculate the gravitational energy density, gravitational temperature, and
gravitational entropy of the Kerr spacetime. We find that in the frame we
consider, Clifton et al.'s estimator does not reproduce the Bekenstein-Hawking
entropy of a Kerr black hole. The results are compared with previous estimates
obtained by the authors using the Rudjord-Gr$\varnothing$n-Hervik approach. We
conclude that the latter represents better the expected behaviour of the
gravitational entropy of black holes.
