Einstein manifolds in Ashtekar variables: explicit examples

TL;DR

This paper demonstrates that all vacuum Einstein solutions can be represented as instanton configurations in Ashtekar variables, providing explicit examples and a systematic approach to generate new solutions.

Contribution

It establishes a mapping between vacuum Einstein solutions and Ashtekar instantons, offering explicit examples and a method to find new solutions.

Findings

Explicit forms of Einstein solutions as Ashtekar instantons

Systematic method for generating new instanton solutions

Examples of novel solutions derived from the approach

Abstract

We show that all solutions to the vacuum Einstein field equations may be mapped to instanton configurations of the Ashtekar variables. These solutions are characterized by properties of the moduli space of the instantons. We exhibit explicit forms of these configurations for several well-known solutions, and indicate a systematic way to get new ones. Some interesting examples of these new solutions are described.