New spherically symmetric solutions in the Einstein–Yang–Mills–Higgs model

Abstract

We study classical solutions in the SU(2) Einstein–Yang–Mills–Higgs theory. The spherically symmetric ansatz for all fields are given, and the equations of motion are derived as a system of ordinary differential equations. The asymptotics and the boundary conditions at the space origin for regular solutions and at the event horizon for black hole solutions are studied. Using the shooting method, we found numerical solutions to the theory. For regular solutions, we find two new sets of asymptotically flat solutions. Each of these sets contains continua of solutions in the parameter space spanned by the shooting parameters. The solutions bifurcate along these parameter curves, and the bifurcations are argued to be due to the internal structure of the model. Both sets of the solutions are asymptotically flat, but one is exponentially so and the other is so with oscillations. For black holes, a new set of boundary conditions is studied, and it is found that there also exists a continuum of black hole solutions in parameter space and similar bifurcation behavior is also present to these solutions. The SU(2) charges of these solutions are found to be zero, and these solutions are proven to be unstable.