paper

Information versus stability in an anti-de Sitter black hole

arXiv:1907.05756 · doi:10.1016/j.physletb.2019.134919

Abstract

Information entropies associated with the energy density in position and momentum spaces are build for an anti-de Sitter (AdS) black hole. These quantities, that satisfy an entropic uncertainty relation, vary with the temperature. The higher is the black hole temperature, the greater/smaller is the information encoded respectively in the position/momentum distributions of energy. On the other hand, as it is well know, AdS black holes are subject to the Hawking Page phase transition. The amplitude for dominance of the black hole phase over the thermal AdS phase increases with the temperature. So, as the system becomes more stable, there is a change in the way that information is stored. In particular: information stored in the spatial energy density increases while information stored in the energy density in momentum space decreases.

In this version V2: more discussions and clarifications. In particular, at the end of the introduction we now explain in which sense can one interpret the entropies defined from energy densities as representing information. Many important references included. One more figure added. 5 pages, 2 figures. Version to appear in Physics Letters B

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