Internal structure of the Skyrme black hole

We consider the internal structure of the Skyrme black hole under a static and spherically symmetric ansatz. We concentrate on solutions with node number 1 and with “winding” number 0, where there exist two solutions for each horizon radius; one solution is stable and the other is unstable against linear perturbation. We find that a generic solution exhibits an oscillating behavior near the singularity, similar to a solution in the Einstein-Yang-Mills (EYM) system, and independent of the stability of the solution. Comparing it with that in the EYM system, this oscillation becomes mild because of the mass term of the Skyrme field. We also find Schwarzschild-like exceptional solutions where no oscillating behavior is seen. Contrary to the EYM system where there is one such solution branch if the node number is fixed, there are two branches corresponding to the stable and unstable ones.