Complex Geometry of Nature and General Relativity

TL;DR

This paper introduces holomorphic methods in general relativity, focusing on complex manifolds, spinor and twistor techniques, and heaven spaces, summarizing thirty years of research in the field.

Contribution

It provides a self-contained overview of complex geometric approaches in general relativity, integrating various methods developed over three decades.

Findings

Holomorphic methods offer new insights into spacetime structure.

Spinor and twistor techniques facilitate the analysis of gravitational fields.

Complex geometry plays a crucial role in understanding solutions to Einstein's equations.

Abstract

An attempt is made of giving a self-contained introduction to holomorphic ideas in general relativity, following work over the last thirty years by several authors. The main topics are complex manifolds, spinor and twistor methods, heaven spaces.