Linear stability of nonrelativistic Proca stars

TL;DR

This paper investigates the linear stability of nonrelativistic Proca stars, demonstrating ground state stability and identifying several stable excited states with potential implications for dark matter models.

Contribution

It provides the first comprehensive analysis of stability for excited states of nonrelativistic Proca stars using combined analytic and numerical methods.

Findings

Ground state of Proca stars is always mode-stable.

Several excited states are also mode-stable, including stationary and multi-frequency states.

Stable excited states could influence ultralight dark matter theories.

Abstract

We study the linear stability of nonrelativistic Proca stars under generic perturbations. Using a combination of analytic and numerical methods, we demonstrate that, as expected, the ground state is always mode-stable. Additionally, we identify several mode-stable spherically symmetric excited states, including stationary states of constant and radial polarization, as well as multi-frequency states in case that the spin-spin selfinteraction vanishes. The existence of stable excited states may have implications for spin-$1$ ultralight dark matter models.