Comment on "Unruh effect for neutrinos interacting with accelerated matter"

TL;DR

This Comment challenges Dvornikov's JHEP analysis of neutrinos in uniformly accelerated matter by pinpointing a foundational error in the curved-space Dirac equation: the effective external current must be expressed with vierbeins, $J^\mu(x)=e^{\mu}_{\ b}(x)J^b$, not as a flat-space quantity. The author derives the correct second-order (quadratic) Dirac equation in Rindler spacetime, showing it reduces to a Whittaker equation with parameters $\bar{\kappa}=E|V|/(a\kappa)$ and $\bar{\mu}=1/2- i\sigma E/a$, and that the true scalar solutions are Whittaker functions of the $M$-type, expressed as $\bar{\varphi}_{\sigma,s}(\rho)=\bar{M}_{\bar{\kappa},\bar{\mu}}(\rho)/\sqrt{\rho}$ with $\rho=2\kappa z$. This corrected treatment yields different infrared/Unruh-like behavior for massive neutrinos in accelerated matter and resolves inconsistencies in the previous ultrarelativistic limit. The work highlights the necessity of a consistent tetrad-based formulation when analyzing Dirac fermions in curved or noninertial backgrounds and provides analytic Whittaker-function solutions for the corrected problem.

Abstract

In the present comment, we show that the fundamental equation worked by Dvornikov in his paper, which is the Dirac equation for a massive neutrino interacting with linearly accelerated matter, is incorrect. In particular, Dvornikov incorrectly wrote/defined the effective external current in a curved space-time. In other words, Dvornikov wrote/defined such an effective current in a flat space-time, which is a mistake. Consequently, the second-order differential equation (generated through the quadratic Dirac equation) in your paper is incorrect, where such an equation is given by the Whittaker equation. So, since the solutions of such a differential equation (whose solutions are the Whittaker functions) are the basis for its results, it implies that such results are also incorrect. In this way, starting from the true/correct Dirac equation with an effective external current in a curved space-time, we obtain in detail the second-order differential equation (also a Whittaker equation) and its solutions for a neutrino interacting with linearly accelerated matter.