Extremal Surfaces in Asymptotically AdS Charged Boson Stars Backgrounds

TL;DR

This paper investigates extremal surfaces in charged boson star backgrounds within AdS spacetime, revealing phase transitions, potential instabilities, and implications for holographic entanglement entropy and dual reduced density matrices.

Contribution

It provides the first detailed analysis of extremal surfaces in charged boson star backgrounds, identifying conditions for phase transitions and possible instabilities.

Findings

Families of minimal surfaces can fail to cover the entire bulk.

A phase diagram of transition regimes is constructed.

Potential instability of hollow boson star solutions is suggested.

Abstract

In this paper, inspired by the holographic dual of the entanglement entropy, we consider the behaviour of extremal, codimension two, spacelike surfaces in the background of three and four dimensional charged boson stars in asymptotically anti-de Sitter spacetime. We find conditions for which families of minimal area surfaces fail to contain the entire bulk spacetime and construct a phase diagram showcasing the transition between regimes. In addition, we use the relation between the star's mass and the central density of the scalar field to argue for a possible instability of such hollow solutions. Finally, we discuss the consequences of our findings for the study of holographic duals of reduced density matrices.