# No-go theorem for static boson stars

## TL;DR

This paper proves a no-go theorem showing that certain static scalar fields cannot form stable, spherically symmetric, asymptotically flat boson star configurations, especially those with monotonically increasing potentials.

## Contribution

It establishes a rigorous theorem that rules out the existence of static boson stars with specific scalar field potentials, clarifying limitations in boson star models.

## Key findings

- Static scalar fields with increasing potentials cannot form spherically symmetric boson stars.
- The theorem applies to nonlinear massive scalar fields.
- No regular static boson star solutions exist under these conditions.

## Abstract

It is proved that self-gravitating static scalar fields whose self-interaction potential $V(\psi^2)$ is a monotonically increasing function of its argument cannot form spherically symmetric asymptotically flat bound matter configurations. Our compact theorem rules out, in particular, the existence of spatially regular static boson stars made of nonlinear massive scalar fields.