Stable black hole solutions with non-Abelian fields

We construct finite mass, asymptotically flat black hole solutions in $d=4$ Einstein—Yang-Mills theory augmented with higher order curvature terms of the gauge field. They possess non-Abelian hair in addition to Coulomb electric charge, and, below some nonzero critical temperature, they are thermodynamically preferred over the Reissner-Nordström solution. Our results indicate the existence of hairy non-Abelian black holes which are stable under linear, spherically symmetric perturbations.

Figure 1

The profiles of a typical non-Abelian nodeless solution are shown together with the corresponding potentials for the perturbation Eqs. (12, 14) below.

Figure 2

The scaled horizon area $a_H=A_H/Q^2$ is plotted $vs$. the scaled temperature $t_H=T_{H}Q$ for several values of the ratio $\kappa =\tau /Q^2$.

Figure 3

The scaled free energy $f=F/Q$ is plotted $vs$. the scaled temperature $t_H=T_{H}Q$ for several values of $\kappa =\tau /Q^2$. The inset shows the behavior of the order parameter $J$ which enters the asymptotics of the magnetic potential.