The Relation Between Technique of Conformal Flat and Damour-Ruffini-Zhao's Method

TL;DR

This paper explores the relationship between the conformal flat technique and Damour-Ruffini-Zhao's method, showing they agree under specific metric conditions but differ in general cases.

Contribution

It clarifies the conditions under which these two methods produce equivalent results and highlights their differences in general scenarios.

Findings

The two methods yield identical results for metrics with $g_{\alpha\beta}=0$ for certain indices.

They are not equivalent for more general metric forms.

The paper provides insight into the applicability of each method depending on the metric structure.

Abstract

The relation between the technique of conformal flat and Damour-Ruffini-Zhao's method is investigated in this paper. It is pointed out that the two methods give the same results when the metric has the form $g_{\alpha\beta=0},$ with $\alpha=0,1$ and $\beta=2,3$. It is indicated that the two methods are not equivalent for general case.