# Studies of a general flat space/boson star transition model in a box through a language similar to holographic superconductors

## TL;DR

This paper investigates phase transitions between flat space and boson stars in a box using holographic superconductor techniques, revealing how scalar parameters influence transition properties and establishing an analytical relation consistent with mean field theory.

## Contribution

It introduces a novel approach applying holographic superconductor methods to flat space/boson star transitions, identifying key parameters and deriving an analytical relation for the order parameter.

## Key findings

- Scalar mass, charge, and St"uckelberg mechanism affect critical points and transition order.
- Transition properties in quasi-local gravity resemble those in holographic superconductors.
- Derived an analytical relation  (5 - 5_c)^{1/2} consistent with mean field theory.

## Abstract

We study a general flat space/boson star transition model in quasi-local ensemble through approaches familiar from holographic superconductor theories. We manage to find a parameter $\psi_{2}$, which is proved to be useful in disclosing properties of phase transitions. In this work, we explore effects of the scalar mass, scalar charge and St$\ddot{u}$ckelberg mechanism on the critical phase transition points and the order of transitions mainly from behaviors of the parameter $\psi_{2}$. We mention that properties of transitions in quasi-local gravity are strikingly similar to those in holographic superconductor models. We also obtain an analytical relation $\psi_{2}\varpropto(\mu-\mu_{c})^{1/2}$, which also holds for the condensed scalar operator in the holographic insulator/superconductor system in accordance with mean field theories.