BTZ Black Hole in Fisher Information Spacetime

TL;DR

This paper explores the representation of BTZ black holes within Fisher information spacetime, linking entanglement spectra to black hole geometry and temperature in the context of AdS/CFT correspondence.

Contribution

It demonstrates a mathematical connection between entanglement spectra and Fisher geometry that models BTZ black holes, highlighting the role of inverse temperature as the horizon position.

Findings

Entanglement spectra define Fisher geometry as black hole spacetime.

Representation resembles finite-temperature conformal field theory spectra.

Inverse temperature maps to the event horizon position.

Abstract

We examine whether we can make a black hole in Fisher information spacetime and what kind of quantum states produce the black hole solution in terms of the anti-de Sitter spacetime/conformal field theory correspondence. Here we focus on the Banados-Teitelboim-Zanelli black hole. There exists a mathematical representation of entanglement spectra that define the Fisher geometry as the black hole spacetime. We find that this representation is quite similar to the entanglement spectra in a conformal field theory at finite temperature except for minor corrections, and then the inverse temperature corresponds to the position of the event horizon in the Poincare coordinate.