Non-trivial, static, geodesically complete, vacuum space-times with a negative cosmological constant

TL;DR

This paper constructs numerous new static, singularity-free vacuum solutions to Einstein's equations with negative cosmological constant, including black hole and non-black hole spacetimes, and proves related uniqueness theorems.

Contribution

It introduces new classes of static, geodesically complete vacuum space-times with negative cosmological constant, expanding the known solution landscape.

Findings

Constructed large families of singularity-free static solutions

Included solutions with and without black hole regions

Established two uniqueness theorems for these solutions

Abstract

We construct a large class of new singularity-free static Lorentzian four-dimensional solutions of the vacuum Einstein equations with a negative cosmological constant. The new families of metrics contain space-times with, or without, black hole regions. Two uniqueness results are also established.