Dirac Spinor Waves and Solitons in Anisotropic Taub-NUT Spaces

TL;DR

This paper develops a new method using anholonomic frames to find exact solutions of Einstein-Dirac equations in five-dimensional anisotropic Taub-NUT spacetimes, revealing how spinor matter can induce gravitational solitons.

Contribution

It introduces a novel approach with anholonomic frames to construct exact 5D Einstein-Dirac solutions and explores their relation to gravitational solitons.

Findings

New classes of exact solutions in 5D gravity with anisotropic Taub-NUT metrics.

Self-consistent Dirac wave packet propagation in anisotropic spacetimes.

Induction of gravitational solitons by spinor matter configurations.

Abstract

We apply a new general method of anholonomic frames with associated nonlinear connection structure to construct new classes of exact solutions of Einstein-Dirac equations in five dimensional (5D)gravity. Such solutions are parametrized by off-diagonal metrics in coordinate (holonomic) bases, or, equivalently, by diagonal metrics given with respect to some anholonomic frames (pentads, or funfbiends, satisfing corresponding constraint relations). We consider two possibilities of generalization of the Taub NUT metric in order to obtain vacuum solutions of 5D Einsitein equations with effective renormalization of constants having distinguished anisotropies on an angular parameter or on extra dimension coordinate. The constructions are extended to solutions describing self-consistent propagations of 3D Dirac wave packets in 5D anisotropic Taub NUT spacetimes. We show that such anisotropic configurations of spinor matter can induce gravitational 3D solitons being solutions of Kadomtsev-Petviashvili or of sine-Gordon equations.