.
Bousso's holographic bound
A simple generalization of the black hole entropy bound (cf. holographic principle) to generic systems is that, in quantum gravity, the maximum entropy which can be enclosed by a spatial boundary is given by a quarter of its surface area. However, as a general rule, this simple generalization appears to be false, because the spatial boundary can be taken to be within the event horizon of a black hole. It also fails in cosmological models.
Raphael Bousso came up with a modification that the spatial boundary should not be a trapped surface. This led him to come up with Bousso's holographic bound,[1][2][3] also known as the covariant entropy bound. Basically, a spatial boundary is valid if, when one considers both null sheets orthogonal to its tangent space, the expansion factors both point in the same direction. This defines inside and outside. The entropy of the interior region is bounded by the surface area of the boundary.
References
Bousso, Raphael (13 August 1999). "A Covariant Entropy Conjecture". Journal of High Energy Physics (7). arXiv:hep-th/9905177. Bibcode:1999JHEP...07..004B. doi:10.1088/1126-6708/1999/07/004.
Bousso, Raphael (9 August 1999). "Holography in General Space-times". Journal of High Energy Physics (6). arXiv:hep-th/9906022. Bibcode:1999JHEP...06..028B. doi:10.1088/1126-6708/1999/06/028. Archived from the original on 24 June 1999.
Bousso, Raphael (5 August 2002). "The holographic principle". Review of Modern Physics 74 (3): 825–874. arXiv:hep-th/0203101. Bibcode:2002RvMP...74..825B. doi:10.1103/RevModPhys.74.825.
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