Abstract

We study axially symmetric multi-soliton solutions of a complex scalar field theory with a sextic potential, minimally coupled to Einstein's gravity. These solutions carry no angular momentum and can be classified by the number of nodes of the scalar field, $k_z$, along the symmetry axis; they are interpreted as chains with $k_z+1$ boson stars, bound by gravity, but kept apart by repulsive scalar interactions. Chains with an odd number of constituents show a spiraling behavior for their ADM mass (and Noether charge) in terms of their angular frequency, similarly to a single fundamental boson star, as long as the gravitational coupling is small; for larger coupling, however, the inner part of the spiral is replaced by a merging with the fundamental branch of radially excited spherical boson stars. Chains with an even number of constituents exhibit a truncated spiral pattern, with only two or three branches, ending at a limiting solution with finite values of ADM mass and Noether charge.

Highlights

  • Many nonlinear physical systems support nontopological solitons, which represent spatially localized field configurations

  • Chains with an odd number of constituents show a spiraling behavior for their Arnowitt-Deser-Misner (ADM) mass in terms of their angular frequency, to a single fundamental boson star, as long as the gravitational coupling is small; for larger coupling, the inner part of the spiral is replaced by a merging with the fundamental branch of radially excited spherical boson stars

  • The chains emerge from the vacuum φ 1⁄4 0 at a maximal value of the boson field frequency ω, which is given by the field’s mass

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Summary

INTRODUCTION

Many nonlinear physical systems support nontopological solitons, which represent spatially localized field configurations. When Q-balls are coupled to gravity, the so-called boson stars (BSs) emerge, which represent solitonic solutions with a topologically trivial and globally regular geometry The simplest such configurations are static and spherically symmetric, the scalar field possessing a mass term only, without self-interaction [4,5]. These solutions are usually dubbed mini-boson stars (mBS), being regarded as macroscopic quantum states, which are prevented from gravitationally collapsing by Heisenberg’s uncertainty principle; they do not have a regular flat spacetime limit.

THE MODEL
The ansatz and equations
Boundary conditions
Numerical method
Nodal structure and energy distribution
The ω-dependence and the branch structure
Even chains
Odd chains
CONCLUSIONS
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