Black lens in a bubble of nothing

Abstract

Applying the inverse scattering method to static and biaxisymmetric Einstein equations, we construct a nonrotating black lens inside a bubble of nothing whose horizon is topologically lens space, $L(n,1)={S}^{3}/{\mathbb{Z}}_{n}$. Using this solution, we discuss whether a static black lens can be in equilibrium by the force balance between the expansion and gravitational attraction.