Constructing black hole entropy from gravitational collapse

Based on a recent proposal for the gravitational entropy of free gravitational fields, we investigate the thermodynamic properties of black hole formation through gravitational collapse in the framework of the semitetrad 1 + 1 + 2 covariant formalism. In the simplest case of an Oppenheimer-Snyder-Datt collapse, we prove that the change in gravitational entropy outside a collapsing body is related to the variation of the surface area of the body itself, even before the formation of horizons. As a result, we are able to relate the Bekenstein-Hawking entropy of the black hole end state to the variation of the vacuum gravitational entropy outside the collapsing body.