Analytical solution of the neutrino wave equation in Kerr geometry with Vaidya-Patel coordinates

TL;DR

This paper presents an exact analytical solution to the Weyl neutrino wave equation in Kerr spacetime using Newman-Penrose calculus, revealing neutrino current asymmetry, which was previously only approximated.

Contribution

It provides the first exact solution of the Weyl neutrino equation in Kerr geometry, advancing understanding of neutrino behavior in curved spacetime.

Findings

Neutrino current asymmetry is demonstrated in the solution.

Exact analytical solutions are obtained, surpassing previous asymptotic or approximate methods.

The approach utilizes the Newman-Penrose formalism in Vaidya-Patel coordinates.

Abstract

Analytical solution of Weyl neutrino wave equation in Kerr geometry is presented by making use of the two-spinor component spin-coefficient Newman-Penrose (NP) calculus. So far only asymptotic or approximate solutions have been found for the Weyl equation in this background. It is shown that neutrino current asymmetry is also present in this solution.