Boson Stars with Vector Meson Exchange Repulsive Interaction

Spherically symmetric static boson stars are solutions of the system of equations of Klein-Gordon equation which is coupled to the Einstein and Proca equation with complex scalar field with U(1) gauge symmetry. In this work, we do not solve these equations directly but first we solve simultaneous equations Klein-Gordon and Proca in flat space-time numerically to obtain interacting boson equation of state (EOS), then we "boost" the corresponding EOS to curved space-time so that, we can solve Einstein equations. If we assume that the distribution of boson in boson stars is inhomogeneous, the boosted EOS is anisotropic in the sense that the pressure to the tangential direction is not the same as the one in the radial direction. We find numerically solutions to see the EOS which are formed in boson stars as the consequence of inhomogeneous assumption. We have found that there is no physically stable solution for inhomogeneous EOS. However, if we assume that the distribution of bosons in matter is homogeneous, we can get a stable solution for static boson stars.