Comment on "Galvano-rotational effect induced by electroweak interactions in pulsars"

TL;DR

This paper corrects a fundamental error in a previous study on neutrino energy spectra in rotating frames, providing an accurate derivation based on the proper Dirac equation in curved space-time.

Contribution

It identifies and corrects the incorrect interaction term used in the prior work, deriving the proper neutrino energy spectrum in a rotating frame from the correct Dirac equation.

Findings

The correct energy spectrum differs significantly from the previous one.

The spectrum is derived from a Bessel equation with a hard-wall potential.

Terms outside the square root in the spectrum are consistent with previous results.

Abstract

In this comment, we show that the fundamental equation worked by Dvornikov in his paper is incorrect, which is given by the Dirac equation for a neutrino interacting with matter in a rotating frame (or curved space-time). In particular, Dvornikov incorrectly wrote/defined the interaction term (effective potentials or background matter) in a curved space-time. Consequently, one of his main results (if not the main one), namely the relativistic energy spectrum, is also incorrect (actually partially incorrect). So, starting from the correct Dirac equation with effective potentials in a curved space-time, we obtain the correct energy spectrum for a neutrino interacting with matter in a rotating frame. We observe that the square root of this spectrum is very different from that obtained by Dvornikov. In fact, in our case, the spectrum was obtained from a Bessel equation subject to a hard-wall confining potential, while the Dvornikov spectrum was obtained from an associated Laguerre equation. However, we note that the only correct thing in the Dvornikov spectrum are the terms outside the square root, which agree with those of the correct spectrum.