Reply to "Comment on 'Can accretion disk properties observationally distinguish black holes from naked singularities?'"

TL;DR

This paper responds to a comment on previous work by clarifying that the metric in question does not satisfy Einstein's equations with a scalar field, discusses a rotating solution generalizing Kerr, and highlights its potential for distinguishing black holes from naked singularities.

Contribution

The authors clarify the limitations of the metric used in prior studies, introduce a rotating scalar field solution, and emphasize its application in testing black hole versus naked singularity models.

Findings

The metric does not satisfy Einstein's equations with a minimally coupled scalar field.

A rotating solution generalizing Kerr for a nonminimally coupled scalar field exists.

The generalized metric can be used to differentiate black holes from naked singularities.

Abstract

In the Comment on "Can accretion disk properties observationally distinguish black holes from naked singularities?", by Bertrand Chauvineau, Phys. Rev. D {\bf 98}, 088501 (2018), the author did show that the metric used in Z. Kov\'{a}cs and T. Harko, Phys. Rev. D {\bf 82}, 124047 (2010), and initially introduced in K. D. Krori and D. R. Bhattacharjee, J. Math. Phys. \textbf{23}, 637 (1982) and K. K. Nandi, P. M. Alsing, J. C. Evans, and T. B. Nayak, Phys. Rev. D \textbf{63}, 084027 (2001), does not satisfy the Einstein gravitational field equations with a minimally coupled scalar field. In our reply we would like to point out that this result is actually not new, but it was already published in the literature. Moreover, a rotating solution that generalizes the Kerr metric for a nonminimally coupled scalar field does exist. We briefly discuss the nature of the singularities for the generalized metric, and point out that it can be used as a testing ground to differentiate black holes from naked singularities. We also mention the existence of some other typing or technical errors existing in the literature.