# Weyl fermions in a family of G\"{o}del-type geometries with a topological defect

## TL;DR

This paper investigates Weyl fermions in G"odel-type spacetimes with topological defects, solving the Weyl equation to reveal how defects alter energy spectra and zero modes in these geometries.

## Contribution

It provides explicit solutions for Weyl fermions in G"odel-type geometries with topological defects, highlighting spectral modifications due to the defects.

## Key findings

- Topological defects modify the energy spectrum of Weyl fermions.
- Zero energy modes are identified in all G"odel-type geometries.
- Explicit eigenspinors and eigenvalues are obtained for the studied geometries.

## Abstract

In this paper we study Weyl fermions in a family of G\"odel-type geometries in Einstein general relativity. We also consider that these solutions are embedded in a topological defect background. We solve the Weyl equation and find the energy eigenvalues and eigenspinors for all three cases of G\"odel-type geometries where a topological defect is passing through them. We show that the presence of a topological in these geometries contributes to modification of the spectrum of energy. The energy zero modes for all three cases of the G\"odel geometries are discussed.