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

TL;DR

This paper constructs and analyzes static black hole solutions in higher-dimensional Einstein-Skyrme theories with scalar potentials and non-positive cosmological constant, exploring their properties, existence, and stability.

Contribution

It introduces new static black hole solutions in higher dimensions with scalar hair, proving their global existence and analyzing their linear stability.

Findings

Solutions exist globally with finite energy for non-positive cosmological constant.

Some solutions are shown to be linearly stable.

Other solutions exhibit linear instability.

Abstract

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.