A Covariant Entropy Conjecture

TL;DR

This paper proposes a universal covariant entropy bound in all Einstein space-times, linking surface area to entropy, with implications for fundamental limits on degrees of freedom in the universe.

Contribution

It introduces a new covariant entropy conjecture applicable to all Einstein space-times, extending previous bounds and connecting to fundamental degrees of freedom.

Findings

The bound can be saturated in cosmological solutions.

The bound is valid inside black holes.

It reduces to Bekenstein's bound for systems with limited self-gravity.

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 geodesics with non-positive expansion. Let S be the entropy on L. Then S does not exceed 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. Thus it places a fundamental limit on the number of degrees of freedom in nature.