Numerical Study Of Boson Stars

In 1955,J.A.Wheeler sought to construct stable,particle-like solutions from only the classical fields of electromagnetism coupled to general relativity,and the solutions was called geons.In 1968,D.J.Kaup replaced electromagnetism with a complex scalar field and found Klein-Gordon geons.They studied the problem of the stability of the resulting boson stars with respect to radial perturbations.In 1969,R.Ruffini used field quantisation of a real scalar field and considered the ground state of N particles.Theoretically,such configurations are known as boson stars.Moreover,astronomical observations indicate that stars rotate too fast around the center of the galaxy to be bound by Newtonian gravity if all matter is visible.This issue,known as the rotation curves problem,implies within the context of Einstein general relativity,that a great amount of the matter in the galaxy is invisible.If we describe the dark matter as a scalar field,the scalar field dark matter model can avoid the problems that weakly interacting massive parti-cles present at a galactic level.Because of the viability presented by the scalar field dark matter model,it is stimulating to go further on testing it.For instance,the model has to reproduce the observed rotation curves of galaxies.At this point boson stars objects could play an important role.For the ground state boson stars,these structures could produce rotation curves,but the rotation curves are not flat enough at large radii.Moreover,the excited state boson stars typically produce a more physically realistic,flatter rotation curves,for which the solutions are unstable In 2010,A.Bernal et al.[1]have obtained the configurations with two states,a ground and a first existed state,and they have demonstrated that the rotation curves of multistate boson stars are flatter at large radii than the rotation curves of single boson stars.As discussed above,the case of multistate boson stars is the spherically symmetric,For the axisymmetric,rotating multistate solutions,however,we believe that the rotation curves of rotating multistate boson stars also are flatter at large radii than the rotation curves of single rotating solutions.Therefore,we especially study the axisymmetric,rotating multistate solutions.In Sec.1,we give a brief review on Klein-Gordon equation and boson star models,including newtonian boson stars,charged boson stars and fermion-boson stars.Moreover,we introduce the models of boson stars with self-interacting potentialIn Sec.2,we construct rotating boson stars composed of the coexisting states of two scalar fields.We found that the rotating boson stars with two states have two types of nodes,including the 1S2S and 1S2P states.We study the properties of the mass M of rotating boson stars with two states as a function of the synchronized frequency ?,as well as the nonsynchronized frequency ?2.Through calculation,we found the domain of existence of multistate solutions is similar to the ground state solutionsIn Sec.3,we consider the self-interacting potential,and construct rotating boson stars with the self-interacting.Meanwhile,we also study the properties of the mass M of rotating boson stars with two states as a function of the synchronized frequency ?,as well as the nonsynchronized frequency ?2.We choose the self-interacting potential U(|?1|)?0,U(|?2|)#0,and we exhibit the mass M of the self-interacting multistate boson stars versus the angular momentum J for the synchronized frequency ?.Our results are similar to the free multistate boson stars solutions.