Soliton boson stars, Q-balls and the causal Buchdahl bound

TL;DR

This paper derives analytic and numerical solutions for gravitating Q-balls and soliton boson stars, showing they saturate the Buchdahl limit at high compactness and behave as different objects at lower compactness.

Contribution

It provides a comprehensive analysis of complex scalar solitons, deriving solutions and exploring their properties across various potentials and compactness regimes.

Findings

Objects saturate the Buchdahl limit with causality at high compactness

At low compactness, they behave as mini boson stars stabilized by quantum pressure

The results are robust across different scalar potentials

Abstract

Self-gravitating non-topological solitons whose potential admits multiple vacua are promising candidates for exotic compact objects. Such objects can arise in several extensions of the Standard Model and could be produced in the early Universe. In this work, we focus on objects made from complex scalars (gravitating Q-balls/soliton boson stars), deriving analytic solutions in spherical symmetry and comparing them with fully numerical ones. In the high-compactness limit we find that these objects present an effectively linear equation of state, thus saturating the Buchdahl limit with the causality constraint. Far from that limit, these objects behave either as flat space-time Q-balls or (in the low-compactness limit) as mini boson stars stabilized by quantum pressure. We establish the robustness of this picture by analyzing a variety of potentials (including cosine, quartic and sextic ones).