# No-go theorem for static boson stars with negative cosmological constants

## TL;DR

This paper proves that static, spherically symmetric boson stars cannot exist in asymptotically Anti-de Sitter spacetimes under certain conditions, extending previous no-go theorems to include negative cosmological constants.

## Contribution

It extends the no-go theorem for static boson stars to asymptotically AdS spacetimes with positive semidefinite scalar potentials.

## Key findings

- Static boson stars cannot be constructed in asymptotically AdS with specified conditions.
- The proof generalizes previous flat spacetime results to AdS backgrounds.
- Scalar fields with positive semidefinite, increasing potentials are incompatible with static boson star solutions.

## Abstract

In a recent paper, Hod has proven no-go theorem for asymptotically flat static regular boson stars. In the present work, we extend discussions to the gravity with a negative cosmological constant. We consider a scalar field vanishing at infinity. In the asymptotically AdS background, we show that spherically symmetric regular boson stars cannot be constructed with self-gravitating static scalar fields, whose potential is positive semidefinite and increases with respect to its argument.