Entanglement Negativity and Defect Extremal Surface

TL;DR

This paper introduces a defect extremal surface formula for entanglement negativity in holographic models of black holes, demonstrating its equivalence with the island formula and analyzing negativity dynamics during black hole evaporation.

Contribution

It proposes a new defect extremal surface formula for entanglement negativity and establishes its equivalence with the island formula in AdS/BCFT models.

Findings

Negativity between black holes decreases to zero over time.

Negativity between black hole and radiation remains constant.

Radiation-radiation negativity increases and saturates after Page time.

Abstract

We study entanglement negativity for evaporating black hole based on the holographic model with defect brane. We introduce a defect extremal surface formula for entanglement negativity. Based on partial reduction, we show the equivalence between defect extremal surface formula and island formula for entanglement negativity in AdS$_3$/BCFT$_2$. Extending the study to the model of eternal black hole plus CFT bath, we find that black hole-black hole negativity decreases until vanishing, left black hole-left radiation negativity is always a constant, radiation-radiation negativity increases and then saturates at a time later than Page time. In all the time dependent cases, defect extremal surface formula agrees with island formula.