Regular and black hole solutions in the Einstein–Skyrme theory with 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 configurations in the asymptotically flat spacetime turns to be linearly stable.