Asymptotically Locally Euclidean/Kaluza-Klein Stationary Vacuum Black Holes in 5 Dimensions

TL;DR

This paper constructs new explicit and analytical 5-dimensional black hole solutions with diverse topologies and asymptotic behaviors, demonstrating their uniqueness and analyzing regularity conditions.

Contribution

It introduces novel bi-axisymmetric stationary vacuum black holes in 5D with asymptotically locally Euclidean or Kaluza-Klein geometries, expanding known solution classes.

Findings

New explicit and analytical solutions with lens space and S^1×S^2 asymptotics.

Solutions include black holes with multiple horizon components and various topologies.

Established the uniqueness of these solutions and analyzed conditions for geometric regularity.

Abstract

We produce new examples, both explicit and analytical, of bi-axisymmetric stationary vacuum black holes in 5 dimensions. A novel feature of these solutions is that they are asymptotically locally Euclidean in which spatial cross-sections at infinity have lens space $L(p,q)$ topology, or asymptotically Kaluza-Klein so that spatial cross-sections at infinity are topologically $S^1\times S^2$. These are nondegenerate black holes of cohomogeneity 2, with any number of horizon components, where the horizon cross-section topology is any one of the three admissible types: $S^3$, $S^1\times S^2$, or $L(p,q)$. Uniqueness of these solutions is also established. Our method is to solve the relevant harmonic map problem with prescribed singularities, having target symmetric space $SL(3,\mathbb{R})/SO(3)$. In addition, we analyze the possibility of conical singularities and find a large family for which geometric regularity is guaranteed.