# Information versus stability in an anti-de Sitter black hole

## TL;DR

This paper investigates how information entropy in position and momentum spaces varies with temperature in an anti-de Sitter black hole, revealing a trade-off in information storage during phase transitions.

## Contribution

It introduces a novel analysis of entropic uncertainty relations in AdS black holes and links information distribution changes to phase stability and temperature.

## Key findings

- Information entropy in position space increases with temperature.
- Entropy in momentum space decreases as temperature rises.
- Phase transition correlates with a shift in information storage modes.

## 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.