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arXiv · hep-th/9610086

Entropy of Localized States and Black Hole Evaporation

Ken D. Olum
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Abstract

We call a state "vacuum-bounded" if every measurement performed outside a specified interior region gives the same result as in the vacuum. We compute the maximum entropy of a vacuum-bounded state with a given energy for a one-dimensional model, with the aid of numerical calculations on a lattice. The maximum entropy is larger than it would be for rigid wall boundary conditions by an amount $δS$ which for large energies is less than or approximately $(1/6) ln (L_in T)$, where L_in is the length of the interior region. Assuming that the state resulting from the evaporation of a black hole is similar to a vacuum-bounded state, and that the similarity between vacuum-bounded and rigid-wall-bounded problems extends from 1 to 3 dimensions, we apply these results to the black hole information paradox. We conclude that large amounts of information cannot be emitted in the final explosion of a black hole.

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Ken D. Olum. 1996-11-20. Entropy of Localized States and Black Hole Evaporation. https://doi.org/10.1103/physrevd.55.6168

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