Chains of rotating boson stars with quartic or sextic self-interaction

TL;DR

This study explores chains of rotating boson stars with quartic or sextic self-interactions, revealing how these interactions influence their global properties, ergosphere structures, and stability, with distinct behaviors based on the number of constituents.

Contribution

It introduces numerical constructions of multi-component rotating boson star chains with self-interactions, analyzing their properties and stability, highlighting differences between quartic and sextic interactions.

Findings

Even-numbered chains show spiraling relations, odd-numbered chains show loop structures.

Ergospheres merge into a single one as frequency increases.

Quartic interactions restrict stable solutions more than sextic interactions.

Abstract

This paper investigates chains of rotating boson stars (BSs) within Einstein gravity coupled to a complex scalar field. The model incorporates quartic or sextic self-interactions in the scalar Lagrangian, which support the existence of stationary, solitonic, gravitationally bound solutions. We numerically construct these multi-component systems and investigate how the self-interactions alter their global properties -- specifically the Arnowitt-Deser-Misner (ADM) mass $M$, the angular momentum $J$ and the morphology of their ergospheres. A central result is the distinct dependence of the $(\omega, M)$ and $(\omega, J)$ relations on the parity of the chains. Specifically, systems with an even number of constituents display spiraling curves, while those with an odd number exhibit loop structures. Moreover, we observe that two initially distinct ergospheres merge into a single one as the frequency $\omega$ increases. Our analysis also indicates that the quartic interaction imposes more restrictive existence bounds, particularly for odd-numbered chains, thereby restricting stable configurations to the weak-coupling regime. In contrast, the sextic interaction has a weaker effect and enables stable solutions at substantially stronger couplings.