Entanglement entropy in three dimensional gravity

TL;DR

This paper presents a simplified algebraic method to compute entanglement entropy in three-dimensional gravity using quotient geometries, enabling new insights into various black hole and wormhole spacetimes.

Contribution

It introduces an algebraic approach to calculate geodesic lengths in 3D gravity, simplifying the derivation of holographic entanglement entropy in complex geometries.

Findings

Computed entanglement entropy for rotating BTZ black holes.

Analyzed entanglement in RP2 geon and wormhole geometries.

Explored temporal and spatial dependence of entanglement entropy.

Abstract

The Ryu-Takayanagi and covariant Hubeny-Rangamani-Takayanagi proposals relate entanglement entropy in CFTs with holographic duals to the areas of minimal or extremal surfaces in the bulk geometry. We show how, in three dimensional pure gravity, the relevant regulated geodesic lengths can be obtained by writing a spacetime as a quotient of AdS3, with the problem reduced to a simple purely algebraic calculation. We explain how this works in both Lorentzian and Euclidean formalisms, before illustrating its use to obtain novel results in a number of examples, including rotating BTZ, the RP2 geon, and several wormhole geometries. This includes spatial and temporal dependence of single-interval entanglement entropy, despite these symmetries being broken only behind an event horizon. We also discuss considerations allowing HRT to be derived from analytic continuation of Euclidean computations in certain contexts, and a related class of complexified extremal surfaces.