Spinorial coordinates for Lorentzian 4-metrics

TL;DR

This paper introduces a spinorial coordinate system for Lorentzian 4-metrics, enabling factorization of metric components and analysis of Einstein's equations, linking Lorentzian and complex metrics.

Contribution

It presents a novel spinorial coordinate framework for Lorentzian 4-metrics, facilitating factorization and analysis of Einstein's equations in these coordinates.

Findings

Metric components factorize into complex conjugates in spinorial coordinates

Linearized Einstein equations are studied within this framework

Relationship between Lorentzian and complex 4-metrics is clarified

Abstract

Lorentzian 4-metrics are expressed in spinorial coordinates. In these coordinates the metric components can be factorized into a product of complex conjugate quantities. The linearized theory and Einstein's vacuum field equations are studied using these coordinates. The relationship between Lorentzian and complex 4-metrics is discussed.