Entropy of Localized States and Black Hole Evaporation

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 $\delta S$ which for large energies is less than or approximately $(1/6)ln(L_{i}nT)$, 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.

27 pages, ReVTeX, 5 postscript figures using epsf. Miscellaneous cleanups, one section rewritten for clarity

References in corpus (13)

• Microscopic Origin of the Bekenstein-Hawking Entropy
• Entropy and Area
• Geometric and Renormalized Entropy in Conformal Field Theory
• On Geometric Entropy
• Black Hole Evaporation without Information Loss
• Virtual Black Holes
• Black Hole Horizons and Complementarity
• Comments on information loss and remnants
• Black Hole Horizon Fluctuations
• Breakdown of the semiclassical approximation at the black hole horizon
• Conformally Invariant Boundary Conditions for Dilaton Gravity
• Predictability and Semiclassical Approximation at the onset of Black Hole formation
• On Black Hole Horizon Fluctuations

Cited by in corpus (2)

• Vacuum-Bounded States and the Entropy of Black Hole Evaporation
• Entropy of very low energy localized states