Time-dependent Spinor field in a static cylindrically-symmetric space-time

TL;DR

This paper investigates the behavior of a nonlinear, time-dependent spinor field in a static cylindrically symmetric space-time, revealing restrictions on the metric and field due to energy-momentum tensor components.

Contribution

It introduces an analysis of a nonlinear, time-dependent spinor field in cylindrically symmetric space-time, highlighting new restrictions on metric functions and field behavior.

Findings

Non-diagonal EMT components impose restrictions on metric and spinor fields.

Time-independent spinor fields lead to Bianchi type-I-like restrictions.

Time-dependent fields result in more complex restrictions.

Abstract

Within the scope of a static cylindrically symmetric space-time we study the behavior of a nonlinear spinor field that depends on time and radial coordinates. It is found that the presence of nontrivial non-diagonal components of the energy-momentum tensor (EMT) imposes some restriction on both the metric functions and the spinor field. While for the time independent spinor field there occur three way restrictions resembling the Bianchi type-I Universe, in this case things become more complicated.