A pseudo-spectral approach to constructing rotating boson star spacetimes

We present a novel numerical solver for the systems of coupled non-linear elliptical differential equations. The solver partitions the computational domain into a set of rectangular pseudo-spectral collocation subdomains and is especially well-suited for working with stiff solutions such as almost shell-like solitonic boson stars. The method can be used in any number of dimensions although is practical for one- to three-dimensional problems. We apply the method to rotating and spherically symmetric solitonic boson stars and demonstrate that it displays exponential convergence. In the spherical symmetric case we explore families of almost shell-like solitonic boson stars and get the results that conform with the well-known analytic approximation.