Geodesics connecting end points of time-like interval in asymptotically AdS spacetime

TL;DR

This paper investigates geodesics connecting timelike boundary points in asymptotically AdS spacetimes, revealing that smooth spacelike geodesics can wind around black hole horizons to connect such points, impacting holographic entanglement entropy interpretations.

Contribution

It demonstrates that in Schwarzschild AdS and modified BTZ black holes, spacelike geodesics can connect timelike boundary points via horizon winding, affecting holographic entropy calculations.

Findings

Smooth spacelike geodesics can connect timelike boundary points by horizon winding.

Photon rings in the bulk influence the properties of time-like entanglement entropy.

Implications for the AdS/CFT duality and entanglement entropy calculations.

Abstract

This paper studies the geodesics connecting two time-like separated boundary points in asymptotically anti-de Sitter (AdS) spacetime. We find that in spherically symmetry Schwarzschild AdS black hole, smooth space-like geodesics can connect timelike-separated points by winding around the horizon multiple times. Similar result will also happen in modified BTZ black hole which contains photon ring in the bulk. According to recent holographic proposal on time-like entanglement entropy, our result suggests that, if there is photon ring/sphere in the bulk, then the time-like entanglement entropy AdS3/CFT2 duality may not have an imaginary part and so further understanding may be necessary.