Two boson stars in equilibrium

TL;DR

This paper constructs and analyzes equilibrium configurations of two non-spinning boson stars in general relativity, revealing the balance of gravitational attraction and scalar repulsion enabled by a phase difference, with implications for gravitational lensing.

Contribution

It introduces the first fully non-linear GR solutions for two boson stars in equilibrium, highlighting the necessity of gravity and the role of scalar phase in their stability.

Findings

Equilibrium solutions exist only with gravity, not in flat spacetime.

Proper distance between stars varies with mass and frequency, explained by a simple model.

Solutions exhibit distinctive gravitational lensing properties.

Abstract

We construct and explore the solution space of two non-spinning, mini-boson stars in equilibrium, in fully non-linear General Relativity (GR), minimally coupled to a free, massive, complex scalar field. The equilibrium is due to the balance between the (long range) gravitational attraction and the (short-range) scalar mediated repulsion, the latter enabled by a $\pi$ relative phase. Gravity is \textit{mandatory}; it is shown no similar solutions exist in flat spacetime, replacing gravity by non-linear scalar interactions. We study the variation of the proper distance between the stars with their mass (or oscillation frequency), showing it can be qualitatively captured by a simple analytic model that features the two competing interactions. Finally, we discuss some physical properties of the solutions, including their gravitational lensing.