Asymptotically anti-de Sitter Proca Stars

TL;DR

This paper demonstrates the existence and stability of asymptotically anti-de Sitter Proca stars, extending previous flat-space solutions to AdS backgrounds, with numerical and analytical analysis in four and five dimensions.

Contribution

It introduces new asymptotically AdS Proca star solutions, analyzes their stability, and explores their properties in four and five dimensions, extending prior flat-space models.

Findings

Proca stars exist in asymptotically AdS spacetimes.

They are stable against spherical perturbations within certain frequency ranges.

The solutions extend to higher dimensions, including five-dimensional cases.

Abstract

We show that complex, massive spin-1 fields minimally coupled to Einstein's gravity with a negative cosmological constant, admit asymptotically anti-de Sitter self-gravitating solutions. Focusing on 4-dimensional spacetimes, we start by obtaining analytical solutions in the test-field limit, where the Proca field equations can be solved in a fixed anti-de Sitter background, and then find fully non-linear solutions numerically. These solutions are a natural extension of the recently found asymptotically flat Proca stars and share similar properties with scalar boson stars. In particular, we show that they are stable against spherically symmetric linear perturbations for a range of fundamental frequencies limited by their point of maximum mass. We finish with an overview of the behavior of Proca stars in $5$ dimensions.