Twistors and Nearly Autoparallel Maps

TL;DR

This paper introduces a new framework for defining twistors on curved spaces, exploring nearly autoparallel maps and their relation to Einstein equations, advancing the geometric understanding of spacetime structures.

Contribution

It proposes a novel definition of twistors on curved spaces and investigates nearly autoparallel twistor equations in relation to Einstein's vacuum equations.

Findings

Nearly autoparallel twistor equations are compatible on nc-flat spaces

Nearly autoparallel twistor structures can generate curved spaces

Connections to vacuum Einstein equations are established

Abstract

In this work a proposal for definition of twistors on generic curved spaces is exposed and investigated. We consider superpositions of nearly autoparallel and nearly geodesic maps (nearly conformal maps, nc-maps) of (pseudo-)Riemannian spaces as generalizations of conformal transforms. We introduce the nearly autoparallel twistor equations being compatible on nc-flat spaces and study nearly autoparallel twistor structures generating curved spaces and vacuum Einstein equations.