Static Black Holes of Higher Dimensional Einstein-Skyrme System with General Couplings

We construct hairy static black holes of higher dimensional general coupling Einstein-Skyrme theories with the scalar potential turned on and the cosmological constant is non-positive in which the scalar multiplets satisfy $O(d+1)$ model constraint where $d$ is the spatial dimension of the spacetime and $d\ge 3$. Some physical properties of solutions near the boundaries, namely, near the (event) horizon and in the asymptotic region are discussed. Then, we prove that these black hole solutions exist globally which may have finite energy for non-positive cosmological constant. Finally, we use perturbative method to perform a linear dynamical stability analysis and then, show the existence of stable and unstable solutions in the model.