Linear Stability of Black Holes and Naked Singularities

Round 1

Reviewer 1 Report

In this review paper,  the authors review the linear stability of black holes and naked singularities. What makes significant the manuscript is the discussion on the encoding of the perturbation fields in gauge invariant curvature scalars and the effects of the perturbation on the geometry of the spacetime. These notes follow from a course delivered at the V José Plínio Baptista School of  Cosmology, held at Guarapari (Espírito Santo) Brazil, from September 30th to October 5th, 2021. Therefore, I recommend the paper for publication in the Universe.

Reviewer 2 Report

The paper is interesting and well-written and the subject of the research is topical. The author made a review of the current status of the linear stability of black holes and naked singularities. Also, the standard modal approach was  introduced and used for proving that the naked singularities in the Kerr-Newman family, as well as the inner black hole regions beyond Cauchy horizons, are unstable and therefore unphysical. A treatment of the boundary condition at the timelike boundary was also detailed given. The nonmodal linear stability concept has been introduced, and used to prove that the domain of outer communications of a Schwarzschild black hole with a non-negative cosmological constant satisfies the stronger stability condition, that rules out transient growths of perturbations. Also, was introduced to show that the perturbed black hole settles into a slowly rotating Kerr black hole. Furthermore, there were discussed the encoding of the perturbation fields in gauge invariant curvature scalars and the effects of the perturbation on the geometry of the spacetime. The author states that "These notes follow from a course delivered at the V José Plínio Baptista School of 12 Cosmology, held at Guarapari (Espírito Santo) Brazil, from September 30th to October 5th, 2021".  The paper is well structured and the Reference section contains enough new and suggestive items.

Even if the subject of the paper does not fall within my specific field of research, I believe that the paper deserves to be published in Universe. I have no possibilities to detect plagiarism.

Reviewer 3 Report

This paper is a very good review of results on linear stability in general relativity for most of the singularities that could be obtained. As such is a significant contribution to the field. Being a review, no new result should be expected but this is a kind of work invaluable for people doing research in this field.