Islands and complexity of eternal black hole and radiation subsystems for a doubly holographic model

TL;DR

This paper investigates entanglement islands and volume complexity in a holographic model simulating eternal black holes and radiation, revealing a phase transition at Page time consistent with unitarity.

Contribution

It introduces a holographic setup with defect modes mimicking black hole and radiation systems, analyzing complexity and entanglement phase transitions at Page time.

Findings

Volume jump at Page time indicates a phase transition.

Entanglement entropy follows a Page curve compatible with unitarity.

Complexity exhibits a transition matching covariant proposals.

Abstract

We study the entanglement islands and subsystem volume complexity corresponding to the left/ right entanglement of a conformal defect in $d$-dimensions in Randall-Sundrum (RS) braneworld model with subcritical tension brane. The left and right modes of the defect mimic the eternal black hole and radiation system respectively. Hence the entanglement entropy between the two follows an eternal black hole Page curve which is unitarity compatible. We compute the volumes corresponding to the left and right branes with preferred Ryu-Takanayagi (RT) surfaces at different times, which provide a probe of the subregion complexity of the black hole and the radiation states respectively. An interesting jump in volume is found at Page time, where the entanglement curve is saturated due to the inclusion of the island surfaces. We explain various possibilities of this phase transition in complexity at Page time and argue how these results match with a covariant proposal qualitatively.