Spinor and Twistor Geometry in Einstein Gravity and Finsler Modifications

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.

latex2e, 11pt,v2 on 26 pages; accepted to "Adv. in Appl. Clifford Algebras" with modified title and following referee's recommendations

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• Finsler and Lagrange Geometries in Einstein and String Gravity
• Critical Remarks on Finsler Modifications of Gravity and Cosmology by Zhe Chang and Xin Li
• Bi-metric pseudo-Finslerian spacetimes
• Weak Gravitational Field in Finsler-Randers Space and Raychaudhuri Equation
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Cited by in corpus (1)

• General off-diagonal integrability of metric and nonmetric geometric flow and Finsler-Lagrange-Hamilton modified Einstein equations