A novel approach for slowly rotating Boson Stars

We present solutions to the Einstein-Klein Gordon (EKG) system representing boson stars in the ``slow rotation'' approximation where the form of the metric, relative to the spherically symmetric problem, is mainly modified by the inclusion of the dragging term gtφ while the metric components are angle independent. On the other hand, the complex-valued scalar field that source the boson star is kept angle dependent, but in order to maintain the self-consistency when solving the EKG system, this dependency is averaged out in the Einstein field equations. The topology of the field is toroidal and differs drastically from the spherically symmetric treatment. Under these approximations we are able to reduce the complexity of the equations yielding a system of ordinary differential equations that is conveniently solved numerically without the need of expensive computational resources. We find sequences of solutions and describe some of their physical (global) properties such as, total mass, angular momentum and compactness. We compare our results with the fully rotating non-linear problem (where no approximations are made in the equations while keeping the stationarity, axisymmetry and circularity hypothesis) and show the region of validity of our approximation. Notably, we show that those physical properties differ in the worst scenarios up to $23%$ relative to the full treatment when restricting to the lowest (quantum) numbers =1=m for the rotating boson star. Finally, we analyze the dynamics of particles (geodesics) in the resulting spacetime and compare our results with the full non-linear problem.