Regular and Black Hole Solutions in the Einstein-Skyrme Theory with Negative Cosmological Constant

TL;DR

This paper investigates how a negative cosmological constant influences regular and black hole solutions in Einstein-Skyrme theory, revealing stability changes and solution existence limits.

Contribution

It demonstrates the existence of a maximum negative cosmological constant for solutions and analyzes stability transitions induced by the cosmological constant.

Findings

Maximum cosmological constant for solutions identified

Stability of solutions depends on the cosmological constant value

Unstable solutions can become stable with increasing negative cosmological constant

Abstract

We study spherically symmetric regular and black hole solutions in the Einstein-Skyrme theory with a negative cosmological constant. The Skyrme field configuration depends on the value of the cosmological constant in a similar manner to effectively varying the gravitational constant. We find the maximum value of the cosmological constant above which there exists no solution. The properties of the solutions are discussed in comparison with the asymptotically flat solutions. The stability is investigated in detail by solving the linearly perturbed equation numerically. We show that there exists a critical value of the cosmological constant above which the solution in the branch representing unstable configuration in the asymptotically flat spacetime turns to be linearly stable.