Holographic Entanglement Entropy and the (3+1)-dimensional Topological Black Hole

TL;DR

This paper explores holographic entanglement entropy in a (3+1)-dimensional topological black hole, revealing observer-dependent horizon areas and proposing coordinate choices that align with CFT regions, advancing understanding of holography in higher dimensions.

Contribution

It analyzes the holographic entanglement entropy in higher-dimensional topological black holes, highlighting observer dependence and proposing optimal coordinate systems for holographic calculations.

Findings

Horizon area is observer dependent in (3+1)-dimensional topological black holes.

Holographic entanglement entropy remains unaffected by observer dependence.

Certain coordinate systems are best suited for holographic calculations, matching CFT regions.

Abstract

We investigate the Holographic Entanglement Entropy proposal in the context of the (3+1)-dimensional topological black hole. In contrast to the well-studied (2+1)-dimensional case, the maximal extension for this black hole includes only a single exterior region with its conformal boundary. This immediately raises a puzzle as to how one can view the purification of the dual conformal field theory state in terms of a thermofield double in the usual manner. Motivated by this puzzle, we calculate the horizon area for these black holes and discover that the result is observer dependent. This observer dependence poses a potential issue in applying the holographic entropy proposal. Investigating this we find that, although this observer dependence does not carry over to the holographic entanglement entropy, there is an indication of a coordinate system which is best adapted for the holographic calculation. These coordinates only cover two regions of the spacetime which exactly correspond to the regions of the CFT on which particle modes are well defined and so we see that the holographic calculation in the spacetime is capable of predicting regions of the CFT where particles cannot exist.