Simple sufficient conditions for the generalized covariant entropy bound
Abstract
The generalized covariant entropy bound is the conjecture that for any null hypersurface which is generated by geodesics with nonpositive expansion starting from a spacelike 2surface B and ending in a spacelike 2surface B^{'}, the matter entropy on that hypersurface will not exceed one quarter of the difference in areas, in Planck units, of the two spacelike 2surfaces. We show that this bound can be derived from the following phenomenological assumptions: (i) matter entropy can be described in terms of an entropy current s_{a}; (ii) the gradient of the entropy current is bounded by the energy density, in the sense that k^{a}k^{b}∇_{a}s_{b}⩽2πT_{ab}k^{a}k^{b}/ħ for any null vector k^{a} where T_{ab} is the stress energy tensor; and (iii) the entropy current s_{a} vanishes on the initial 2surface B. We also show that the generalized Bekenstein bound—the conjecture that the entropy of a weakly gravitating isolated matter system will not exceed a constant times the product of its mass and its width—can be derived from our assumptions. Though we note that any local description of entropy has intrinsic limitations, we argue that our assumptions apply in a wide regime. We closely follow the framework of an earlier derivation, but our assumptions take a simpler form, making their validity more transparent in some examples.
 Publication:

Physical Review D
 Pub Date:
 September 2003
 DOI:
 10.1103/PhysRevD.68.064001
 arXiv:
 arXiv:hepth/0305149
 Bibcode:
 2003PhRvD..68f4001B
 Keywords:

 04.20.Cv;
 04.60.m;
 04.70.Dy;
 Fundamental problems and general formalism;
 Quantum gravity;
 Quantum aspects of black holes evaporation thermodynamics;
 High Energy Physics  Theory
 EPrint:
 7 pages, revtex