Spinors in Cylindrically Symmetric Space–Time

Bijan Saha

doi:10.3390/universe6090152

Abstract

We studied the behavior of nonlinear spinor field within the scope of a static cylindrically symmetric space–time. It is found that the energy-momentum tensor (EMT) of the spinor field in this case possesses nontrivial non-diagonal components. The presence of non-diagonal components of the EMT imposes three-way restrictions either on the space–time geometry or on the components of the spinor field or on both. It should be noted that the analogical situation occurs in cosmology when the nonlinear spinor field is exploited as a source of gravitational field given by the Bianchi type-I cosmological model.

Highlights

In recent years spinor field has been used in cosmology by many authors [1,2,3,4,5,6]
We studied a system of nonlinear spinor field minimally coupled to a static cylindrically symmetric space–time
It is found that the energy-momentum tensor (EMT) of the spinor field has nontrivial non-diagonal components

Summary

Introduction

In recent years spinor field has been used in cosmology by many authors [1,2,3,4,5,6]. Except for the Friedmann–Robertson–Walker (FRW) model given in Cartesian coordinates, in all other space–times spinor field possesses nontrivial non-diagonal components of the energy-momentum tensor. As far as static spherically symmetric space–time is concerned, the presence of non-diagonal components of EMT imposes restrictions on the spinor field only [10]. As it was mentioned earlier, recently spinor field is being used in astrophysics Most of these works were done within the scope of static spherically symmetric space–time [10,14,18]. Since a number of astrophysical objects are given by cylindrically symmetric space–time [19] in this report we plan to consider the spinor field within this model.

Basic Equations

Conclusions