Comment on "Exact massless spinor quasibound states of Schwarzschild black hole"

TL;DR

This paper critiques and corrects errors in a previous study on massless spinor states around Schwarzschild black holes, emphasizing proper mathematical formalism in the Dirac equation in curved spacetime.

Contribution

It clarifies the correct mathematical formalism for the Dirac equation in Schwarzschild spacetime, correcting errors in a prior publication.

Findings

Identification of errors in the previous paper's Dirac equation formulation

Correction of the mathematical formalism based on established references

Emphasis on proper use of tetrad fields and gamma matrices in curved spacetime

Abstract

In this comment, we point out a series of errors made by Senjaya in your paper (2024) \cite{Senjaya}. In particular, these errors involved the Dirac equation in the 3+1 dimensional Schwarzschild spacetime, tetrad field, curved gamma matrices, and the time-independent Dirac equation written in terms of the inner/scalar product between the gamma matrices and the orbital angular momentum (i.e., $\vec{\gamma}\cdot\vec{L}$). Besides, the strange/peculiar thing about all this is that even Senjaya \cite{Senjaya} citing Collas and Klein \cite{Collas}, where the (mathematical) formalism is correct, everything indicates that he ``ignored'' or ``forgot'' to use such formalism in your paper. Therefore, using Ref. \cite{Collas}, we show here the correct form of the errors made by Senjaya \cite{Senjaya}.