Clifford Algebroids and Nonholonomic Spinor Deformations of Taub-NUT Spacetimes

TL;DR

This paper introduces a new class of five-dimensional solutions in gravity with Lie algebroid symmetry, describing Dirac wave propagation in deformed Taub-NUT spacetimes, revealing potential higher-dimensional signals and novel symmetries.

Contribution

It develops Clifford nonholonomic algebroid theory and constructs exact 5D Einstein-Dirac solutions with off-diagonal metrics and nonholonomic frames, extending previous models.

Findings

Solutions exhibit polarization constants indicating higher dimensions or torsion effects.

New symmetries generalize Lie algebra structures to nonholonomic Lie algebroids.

Propagate Dirac wave packets in nonholonomically deformed Taub-NUT backgrounds.

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.