Black Hole Singularity and Timelike Entanglement

TL;DR

This paper investigates how timelike and conventional entanglement entropy can serve as probes of black hole singularities within the AdS/CFT framework, revealing unique behaviors near singularities and complex saddle point phenomena.

Contribution

It introduces an analytically solvable example demonstrating characteristic entanglement entropy behavior around black hole singularities and explores complex saddle point contributions beyond standard assumptions.

Findings

Holographic timelike entanglement entropy shows distinctive behavior near singularities.

Multiple complex saddle points influence entanglement entropy calculations.

Standard assumptions like Lewkowycz-Maldacena are sometimes violated in these setups.

Abstract

We study timelike and conventional entanglement entropy as potential probes of black hole singularities via the AdS/CFT correspondence. Using an analytically tractable example, we find characteristic behavior of holographic timelike entanglement entropy when the geometry involves a curvature singularity. We also observe interesting phenomena that, in some particular setups, holographic timelike and conventional entanglement entropy are determined from multiple complex saddle points, which fall outside the assumptions of the Lewkowycz-Maldacena type argument.