Geometric Framework for Entropy in General Relativity

We introduce a covariant and geometrical framework for entropy in relativistic theories. In this framework the entropy of gravitational systems turns out to be a geometric quantity with well-defined cohomological properties arising from the obstruction to foliating spacetime into spacelike hypersurfaces. The framework relies on general covariance within a geometric framework which was recently defined to deal with the variation of conserved quantities generated by N"other theorem. The definition of gravitational entropy so obtained turns out to be very general: it can be generalized to causal horizons and multiple-horizon spacetimes and it can be applied to define entropy for more exotic singular solutions of Einstein field equations. The same definition is also well-suited for higher dimensions and in the case of alternative gravitational theories (e.g. Chern-Simons theories and Lovelock Gravity).