# Proca Q Balls and their Coupling to Gravity

## TL;DR

This paper constructs and analyzes a broad class of spherically symmetric solutions involving Proca Q-balls and stars, exploring their properties, existence domains, and critical phenomena in both flat and gravitational contexts.

## Contribution

It extends the Proca Lagrangian with self-interactions to generate new solutions and thoroughly investigates their parameter space and critical behavior.

## Key findings

- Existence of new Proca Q-ball and star solutions.
- Identification of critical phenomena limiting solution domains.
- Analysis of solutions in both flat and self-gravitating scenarios.

## Abstract

Extending the Proca Lagrangian of a massive complex-valued vector field by self-interaction potential, we construct a large class of spherically symmetric solutions in flat Minkowski background as well as in the self-gravitating case. Our solutions encompass Proca Q-balls and Proca stars known in the literature, but present new features and go beyond the limited region of parameter space charted so far. A special emphasis is set to the domain of existence of the solutions in relation with the coupling constants of the potential and to the critical phenomena limiting this domain.