Asymptotically Flat, Stable Black Hole Solutions in Einstein–Yang-Mills–Chern-Simons Theory

We construct finite mass, asymptotically flat black hole solutions in $d=5$ Einstein–Yang-Mills–Chern-Simons theory. Our results indicate the existence of a second order phase transition between Reissner-Nordström solutions and the non-Abelian black holes which generically are thermodynamically preferred. Some of the non-Abelian configurations are also stable under linear, spherically symmetric perturbations.

Figure 1

The profiles of a typical non-Abelian (dotted line) solution with $\kappa =0.5$ are shown together with the corresponding Reissner-Nordström black hole with the same mass and electric charge parameters $M=4.186$ and $Q=2$, respectively. The inset shows the corresponding potential for the perturbation equation (11) below.

Figure 2

The dimensionless horizon area is plotted vs the scaled temperature for several values of the electric charge and a given value of $\kappa$.

Figure 3

The scaled free energy is plotted vs the scaled temperature for two different values of $\kappa$ and the same charge parameter $Q=3.8$.