Notes on self-dual gravity

TL;DR

This paper explores self-dual gravity using the Newman-Penrose formalism, identifying its solution space, asymptotic symmetries, and transforming specific solutions into a particular gauge.

Contribution

It characterizes the solution space of self-dual gravity and demonstrates that its asymptotic symmetries are the extended BMS group, with explicit transformations of solutions.

Findings

Self-dual gravity's solution space is specified within Newman-Unti solutions.

Asymptotic symmetries of self-dual gravity are extended BMS symmetries.

The self-dual Taub-NUT solution is transformed into the Newman-Unti gauge.

Abstract

In this paper, we study self-dual gravity in the Newman-Penrose formalism. We specify the self-dual solution space from the Newman-Unti solutions. We show that the asymptotic symmetries of the self-dual gravity are still the (extended) BMS symmetries. We transform the self-dual Taub-NUT solution into the Newman-Unti gauge in analytical form.