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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.
Spacetime, Mass, Quantum gravity, Milky Way, Stephen Hawking
Thermodynamics, Energy, Statistical mechanics, Temperature, Thermodynamic system
String theory, Quantum gravity, M-theory, Entropy, Space
Quantum gravity, String theory, Quantum field theory, Renormalization group, M-theory
Quantum gravity, General relativity, Hawking radiation, Jackiw–Teitelboim gravity, Liouville gravity
Inflation (cosmology), Big Bang, Physical cosmology, University of Cambridge, Soviet Union