in a high entropy state because of the thermal equilibrium that prevailed soon after the Big Bang. Hence there must be an entropy associated with the gravitational field and this gravitational entropy must have been initially very low, so that the net entropy (matter plus gravity) becomes extremely small.

Such a gravitational entropy will have to be defined from the Riemann curvature. The Ricci part of the curvature diverges at a Friedmann Big Bang singularity. Since we are interested in a low gravity entropy at the Big Bang, it is plausible that this entropy is related to the Weyl part of the curvature, which is zero at the Friedmann singularity. This has come to be known as the Weyl Curvature Hypothesis: in order to have an explanation of the second law, the Weyl curvature must be zero (or at least negligible compared to the Ricci curvature) at the initial cosmological singularity. It should be said though that a concrete mathematical relation between the Weyl curvature and gravitational entropy has not yet been found.

It is possible to regard a naked singularity forming in collapse as an ‘initial’ singularity, because geodesics terminate in the past at the singularity. Hence it is 