A covariant entropy conjecture

Abstract

We conjecture the following entropy bound to be valid in all space-times admitted by Einstein's equation: let A be the area of any two-dimensional surface. Let L be a hypersurface generated by surface-orthogonal null geodesies with non-positive expansion. Let S be the entropy on L. Then S ≤ A/4. We present evidence that the bound can be saturated, but not exceeded, in cosmological solutions and in the interior of black holes. For systems with limited self-gravity it reduces to Bekenstein's bound. Because the conjecture is manifestly time reversal invariant, its origin cannot be thermodynamic, but must be statistical. It thus places a fundamental limit on the number of degrees of freedom in nature.