Black hole Skyrmion in a generalized Skyrme model

TL;DR

This paper investigates black hole solutions with Skyrme hair in a generalized model including higher-order derivatives, revealing the necessity of the Skyrme term for stability.

Contribution

It introduces a generalized Skyrme model with higher-order derivatives coupled to gravity and analyzes the conditions for stable black hole Skyrme hair.

Findings

The sixth-order derivative term alone cannot stabilize black hole hair.

A sufficiently large Skyrme term coefficient is required for stability.

Black hole Skyrme hair solutions depend critically on the Skyrme term presence.

Abstract

We study a Skyrme-like model with the Skyrme term and a sixth-order derivative term as higher-order terms, coupled to gravity and we construct Schwarzschild black hole Skyrme hair. We find, surprisingly, that the sixth-order derivative term alone cannot stabilize the black hole hair solutions; the Skyrme term with a large enough coefficient is a necessity.