New spherically symmetric solutions in Einstein-Yang-Mills-Higgs model

TL;DR

This paper discovers new spherically symmetric solutions in the Einstein-Yang-Mills-Higgs theory, including regular and black hole solutions, analyzing their properties, stability, and bifurcation behavior through numerical methods.

Contribution

It introduces two new sets of asymptotically flat solutions and explores their bifurcations, expanding understanding of classical solutions in Einstein-Yang-Mills-Higgs models.

Findings

Found two new sets of regular solutions with different asymptotic behaviors.

Discovered continuum of black hole solutions with bifurcation phenomena.

Proved that all solutions have zero SU(2) charge and are unstable.

Abstract

We study classical solutions in the SU(2) Einstein-Yang-Mills-Higgs theory. The spherically symmetric ans\"atze 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 space origin for regular solutions and at 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 bifurcation 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 zero and these solutions are proven to be unstable.