A covariant entropy conjecture
Abstract
We conjecture the following entropy bound to be valid in all spacetimes admitted by Einstein's equation: let A be the area of any twodimensional surface. Let L be a hypersurface generated by surfaceorthogonal null geodesics with nonpositive expansion. Let S be the entropy on L. Then S leq 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 selfgravity 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.
 Publication:

Journal of High Energy Physics
 Pub Date:
 July 1999
 DOI:
 10.1088/11266708/1999/07/004
 arXiv:
 arXiv:hepth/9905177
 Bibcode:
 1999JHEP...07..004B
 Keywords:

 High Energy Physics  Theory;
 Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 41 pages, 7 figures. v2,v3: references added