Addendum: Observational redshift from general spherically symmetric black holes

Abstract

In this addendum, we change the sign of the squared length scale parameter (\(l^2\rightarrow -l^2\)) in the conformal factor presented in Eq. (36) of the original article to explore its effects on the observational frequency shift. We make this change of sign because it removes an unnecessary physical singularity at \(r=l\) from the original expression of the curvature invariants of the conformal metric. Then, we apply this correction to all the equations involving the parameter \(l^2\) and find that under this modification in the conformal mapping, the relations of redshift/blueshift and gravitational redshift change. The new equations are represented in Eqs. (44)–(45) and their behavior are illustrated in Figs. 1, 2 and 3, corresponding to the equations and figures in the original article. Additionally, due to this change of the sign in the squared length scale parameter, we discuss the effects of this parameter on the observational frequency shift which differ from those presented in section 5 of the original article. We also note that the expressions as well as corresponding figures and discussions presented in the original paper are correct for that choice of the conformal factor.