Rotational influence on fermions within negative curvature wormholes

TL;DR

This paper investigates how rotation and negative curvature of wormholes influence the behavior of relativistic fermions, deriving exact solutions and energy expressions to understand their evolution in such exotic spacetimes.

Contribution

It provides the first analytical solutions of the Dirac equation for fermions in rotating negative curvature wormholes, including energy spectra and generalized Weyl fermion results.

Findings

Derived exact energy expressions for fermions in rotating wormholes

Analyzed the impact of rotation and curvature on fermionic field evolution

Generalized results to Weyl fermions in curved, rotating backgrounds

Abstract

In this research, we examine relativistic fermions within the rotating frame of negative curvature wormholes. Initially, as is typical in our context, we introduce the wormholes by embedding a curved surface into a higher dimensional flat Minkowski spacetime. Subsequently, we derive the spacetime metric that characterizes the rotating frame of these wormholes. We then investigate analytical solutions of the generalized Dirac equation within this framework. Through exploring a second-order nonperturbative wave equation, we seek exact solutions for fermions within the rotating frame of hyperbolic and elliptic wormholes, also known as negative curvature wormholes. Our analysis provides closed-form energy expressions, and we generalize our findings to Weyl fermions. By considering the impact of the rotating frame and curvature radius of wormholes, we discuss how these factors affect the evolution of fermionic fields, offering valuable insights into their behavior.