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.
Physical Review D
- Pub Date:
- March 2015
- Fundamental problems and general formalism;
- Singularities and cosmic censorship;
- General Relativity and Quantum Cosmology
- 8 pages, 1 figure