Information versus stability in an anti-de Sitter black hole

Nelson R.F Braga

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 known, 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.

Highlights

It has been proposed by Gleiser and Sowinski [1] that the stability of compact objects can be characterized by a quantity, called configuration entropy, introduced by Gleiser and Stamatopoulos in refs.[2, 3]
We show in figure 1 plots of the entropies f, fand their sum: f + fas a function of the horizon radius divided by the anti-de Sitter (AdS) radius rh/b
One notes that as the horizon radius, and correspondingly the temperature, increase, the entropy in position space f increases while the momentum space entropy fhas the opposite behavior

Summary

INTRODUCTION

It has been proposed by Gleiser and Sowinski [1] that the stability of compact objects can be characterized by a quantity, called configuration entropy, introduced by Gleiser and Stamatopoulos in refs.[2, 3]. In this letter we will build up modal fractions as the normalized square of the energy densities of the AdS black hole, in position and momentum spaces. These quantities are not probability densities if one makes an observation of the energy. For the momentum case one can consider a process of determining the momentum of a particle that has a probability density in momentum space equal to the modal fraction obtained from the energy density in momentum space It is in this sense that we will interpret f and fas representing information content.

HAWKING PAGE TRANSITION

ENERGY DENSITY FOR THE ADS BLACK HOLE

RESULTS AND CONCLUSIONS