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Clifford Algebroids and Nonholonomic Spinor Deformations of Taub-NUT Spacetimes

Sergiu I. Vacaru
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Abstract

In this paper we examine a new class of five dimensional (5D) exact solutions in extra dimension gravity possessing Lie algebroid symmetry. The constructions provide a motivation for the theory of Clifford nonholonomic algebroids elaborated in Ref. hep-th/0501217. Such Einstein-Dirac spacetimes are parametrized by generic off--diagonal metrics and nonholonomic frames (vielbeins) with associated nonlinear connection structure. They describe self-consistent propagations of (3D) Dirac wave packets in 5D nonholonomically deformed Taub NUT spacetimes and have two physically distinct properties: Fist, the metrics are with polarizations of constants which may serve as indirect signals for the presence of higher dimensions and/or nontrivial torsions and nonholonomic gravitational configurations. Second, such Einstein-Dirac solutions are characterized by new type of symmetries defined as generalizations of the Lie algebra structure constants to nonholonomic Lie algebroid and/or Clifford algebroid structure functions.

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Sergiu I. Vacaru. 2005-02-16. Clifford Algebroids and Nonholonomic Spinor Deformations of Taub-NUT Spacetimes. https://arxiv.org/abs/hep-th/0502145

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