Separation of variables and exact solution of the Klein-Gordon and Dirac equations in an open universe

TL;DR

This paper derives asymptotic solutions for the Klein-Gordon and Dirac equations in an open universe with a horn topology under a time-dependent magnetic field, advancing understanding of quantum fields in complex cosmological models.

Contribution

It provides a novel analysis of quantum field equations in an open universe with a horn topology, including asymptotic solutions under time-dependent magnetic fields.

Findings

Asymptotic behavior of solutions analyzed

Solutions characterized for specific cosmological conditions

Insights into quantum fields in complex topologies

Abstract

We solve the Klein-Gordon and Dirac equations in an open cosmological universe with a partially horn topology in the presence of a time dependent magnetic field. Since the exact solution cannot be obtained explicitly for arbitrary time-dependence of the field, we discuss the asymptotic behavior of the solutions with the help of the relativistic Hamilton-Jacobi equation.