# Covariant holographic entanglement negativity for disjoint intervals in $AdS_3/CFT_2$

## TL;DR

This paper proposes a covariant holographic method to compute entanglement negativity for disjoint intervals in time-dependent 1+1 dimensional CFTs, matching replica results and exploring thermalization in black hole formation.

## Contribution

It introduces a new covariant holographic construction for entanglement negativity applicable to dynamic states in $AdS_3/CFT_2$, extending previous static approaches.

## Key findings

- Reproduces replica technique results in large central charge limit.
- Applies to non-static $AdS_3$ geometries including rotating BTZ black holes.
- Analyzes entanglement negativity during black hole formation and thermalization.

## Abstract

We advance a construction for the covariant holographic entanglement negativity for time dependent mixed states of disjoint intervals in $(1+1)$ dimensional conformal field theories ($CFT_{1+1}$) dual to bulk non static $AdS_3$ geometries. Application of our proposal to such mixed states in a $CFT_{1+1}$ dual to bulk non extremal and extremal rotating BTZ black holes exactly reproduces the replica technique results in the large central charge limit. We also investigate the time dependent holographic entanglement negativity for such mixed states in a $CFT_{1+1}$ dual to a bulk Vaidya-$AdS_3$ geometry in the context of their thermalization involving bulk black hole formation.