Extremal Cosmological Black Holes in Horndeski Gravity and the Anti-Evaporation Regime

Round 1

Reviewer 1 Report

In this paper the authors analyze the existence of extremal black hole solutions (Nariai space-time) in the framework of Horndenski gravity and study the phenomenon of antievaporation. The work is interesting: the original work on BH antievaporation was denveloped by Bousso and Hawking (Ref 38) and some results are known in F(R) and F(R, G)-gravity, but in Horndenski gravity are pretty new. The authors show how an effective cosmological constant can be supported by non-trivial solutions of the Horndenski field. The study on perturbations shows the absence of antievaporation in Horndenski gravity. I just would like to point out that the bibliography of the manuscript needs to be reorganized: in the specific, due to the argument of the paper, the seminal works of Nariai and Bousso-Hawking should be shifted at the beginning of bibliography. Then, the paper can be accepted for publication in Universe.

Author Response

Following referee’s advise, we have reorganised the introduction and the references in order to cite the ones corresponding to Nariai spacetime at the beginning.

Reviewer 2 Report

All comments and suggestions are shown in the attached PDF file.

Comments for author File: Comments.pdf

Author Response

Please see attached file.

Author Response File: Author Response.pdf

Reviewer 3 Report

This article attempts to investigate the anti-evaporation of the Nariai black hole solution in the Horndeski theory.

In section 3, the authors have demonstrated the model-by-model analysis in the subsections and confirmed that the Horndeski theory has the Nariai solution.

Considering a particular model that satisfies the recent constraint from the gravitational wave observation, the authors have analyzed the stability of Nariai spacetime and discussed the perturbation of the scalar field in section 4.

This paper is organized concisely and summarized in the self-contained form, and the contents are scientifically significant and exciting enough for the publication.

I could not find major issues from the scientific viewpoint, and the presentation style seems appropriate.

Although this article seems almost ready for publication, I would like to suggest a minor issue.

1) In the introduction, the authors have referred to the earlier works on the anti-evaporation in the modified gravity.

I found several works on the anti-evaporation in the modified gravity which the Horndeski theory does not include.

To complete this manuscript, it seems better to cite the following earlier works:

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Katsuragawa,

``Anti-Evaporation of Black Holes in Bigravity,''

Universe 1 (2015) no.2, 158-172

doi:10.3390/universe1020158

G. L. Nashed,

``Spherically symmetric black hole solution in mimetic gravity and anti-evaporation,''

Int. J. Geom. Meth. Mod. Phys. 15 (2018) no.09, 1850154

doi:10.1142/S0219887818501542

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Author Response

We have included the references mention by the referee and other interesting and related ones we found in the literature.

Round 2

Reviewer 2 Report

The authors showed the solutions suggested in my previous report, and proved that they suffer from the strong coupling where the linear perturbation analysis loses the predictability and cannot be trusted any more. They also properly addressed all the issues raised in my previous report, about the terminology, logic and references.

 I think that now the paper may be accepted by Universe.