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A Covariant Entropy Conjecture

High Energy Physics - Theory 2010-02-03 v3 Astrophysics General Relativity and Quantum Cosmology

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.

Keywords

Cite

@article{arxiv.hep-th/9905177,
  title  = {A Covariant Entropy Conjecture},
  author = {Raphael Bousso},
  journal= {arXiv preprint arXiv:hep-th/9905177},
  year   = {2010}
}

Comments

41 pages, 7 figures. v2,v3: references added