Soliton stars in the breather limit

TL;DR

This paper derives an asymptotic model for soliton stars using the Einstein-Klein-Gordon system, finding a breather-like solution that matches numerical results and predicts a time-periodic redshift near the star's center.

Contribution

It introduces a novel asymptotic reduction of the Einstein-Klein-Gordon system and constructs a breather-like solution using variational methods, aligning with numerical simulations.

Findings

Existence of a breather-like periodic solution

Agreement between analytical and numerical results

Prediction of a time-periodic redshift near the star's center

Abstract

This paper presents an asymptotic reduction of the Einstein-Klein-Gordon system with real scalar field ("soliton star problem"). A periodic solution of the reduced system, similar to the sine-Gordon breather, is obtained by a variational method. This tallies with numerical computations. As a consequence, a time-periodic redshift for sources close to the center of the star is obtained.