Chains of Boson Stars

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.