Spinor and Twistor Geometry in Einstein Gravity and Finsler Modifications

TL;DR

This paper extends spinor and twistor geometry to (pseudo) Riemannian and Finsler spaces with nonholonomic structures, enabling new formulations of Einstein gravity in Finsler-like variables.

Contribution

It introduces a generalized framework for spinor and twistor geometry on nonholonomic and Finsler spaces, connecting these structures to Einstein gravity.

Findings

Defined nonholonomic twistors via generalized twistor equations.

Showed how to globalize local twistor constructions using nonholonomic deformations.

Applied the approach to Einstein gravity with Finsler-like variables.

Abstract

We present a generalization of the spinor and twistor geometry for on (pseudo) Riemannian manifolds enabled with nonholonomic distributions or for Finsler-Cartan spaces modelled on tangent Lorentz bundles. Nonholonomic (Finsler) twistors are defined as solutions of generalized twistor equations determined by spin connections and frames adapted to nonlinear connection structures. We show that the constructions for local twistors can be globalized using nonholonomic deformations with "auxiliary" metric compatible connections completely determined by the metric structure and/or the Finsler fundamental function. We explain how to perform such an approach in the Einstein gravity theory formulated in Finsler like variables with conventional nonholonomic 2+2 splitting.