Aspects of Gauss-Bonnet Scalarisation of Charged Black Holes

Round 1

Reviewer 1 Report

\documentstyle[12pt]{article}
\textwidth 160 mm
\textheight 225 mm
\topmargin -25mm
\hoffset -1cm
\pagestyle{empty}
%\usepackage{color}

\begin{document}

\begin{center}
{\Large\bf {Referee report \\to the paper universe-1492786 entitled\\
{\it "\textit{Aspects of Gauss-Bonnet scalarisation of charged black holes}" \\
by Carlos A. R. Herdeiro, Alexandre M. Pombo and Eugen Radu}}}
\end{center}

The authors of the paper universe-1492786 
are underlining that in the general relativity vacuum black holes (BHs) can be scalarised in models where a scalar field non minimally couples to the Gauss-Bonnet (GB) invariant. Such GB scalarisation comes in two
flavours, depending on the GB sign that triggers the phenomenon.  The authors discuss the GB$^-$
 scalarisation of Reissner-Nordstrom and Kerr-Newman BHs, discussing zero modes and constructing fully
non-linear solutions.  In order to assess the generality of the
observed features, the authors also briefly consider the GB$^\pm$ scalarisation of stringy dilatonic BHs and coloured BHs which provide qualitative differences with respect to the electrovacuum case.

The calculations performed are standard ones and  correct, however, I have the following comments and suggestions:

i) The abstract of the paper has not been well written. Some part of the current version of the abstract looks like an introduction to the topic. 
It would be better if the authors could revise the text of abstract in a form presenting the main results from the
main part of the paper.

ii) The conclusion is written in the way which needs more astrophysical justifications then making
the future prospects with the detailed plan.
I advise the author to summarize in detail the main obtained results with
the discussions on their astrophysical observability.

iii)  The quality and number of plots and figures can be definitely improved and increased, respectively.

iv)  Since the Universe journal is oriented on publication of the papers related to physics the author has to explore
possible astrophysical applications of the obtained results in more concrete way.

 

Since the study of this manuscript is mathematically correct and
indeed of interest in addressing the properties and alternate parameters of black holes I would recommend to the authors 
to revise it along my comments and resubmit the revised version to the journal.
I hope the revised paper would be more suitable for publication in the \textbf{UNIVERSE} journal.

\end{document}

Comments for author File: Comments.pdf

Author Response

We would like to thank the referee for the careful reading of our paper. Below we address the referee's comments.   i) The abstract of the paper has not been well written. Some part of the current version of the abstract looks like an introduction to the topic. 
It would be better if the authors could revise the text of abstract in a form presenting the main results from the
main part of the paper.   In the first part of the abstract, we introduce the idea of GB^+ and GB^- scalarisation (which are known in the literature, but not under this denomination) to contextualize the results. In the second part we summarise the results:  "We discuss the GB$^-$ scalarisation of Reissner-Nordstr\"om and Kerr-Newman BHs, discussing zero modes and constructing fully non-linear solutions. Some comparisons with GB$^+$ scalarisation are given. To assess the generality of the observed features, we also briefly consider the GB$^\pm$ scalarisation of stringy dilatonic BHs and coloured BHs which provide qualitative differences with respect to the electrovacuum case namely on the distribution and existence of regions triggering GB$^-$ scalarisation.
" To comply with the referee's request we have extended the final sentence to be more specific.     ii) The conclusion is written in the way which needs more astrophysical justifications then making the future prospects with the detailed plan.
I advise the author to summarize in detail the main obtained results with
the discussions on their astrophysical observability.   We thank the referee for the remark. However, in our opinion, since the scope of the journal “Universe” covers both field theory and mathematical physics, for example, a connection to astrophysics is not mandatory. Nonetheless, to comply with the referee's request, we have attempted to connect our study to astrophysics by adding a final sentence in the conclusions.   iii)  The quality and number of plots and figures can be definitely improved and increased, respectively.   Since the referee was not specific about which improvements should be made or which plots should be added, we have made small improvements to some of the plots (colours, style, etc) and added one extra plot (new Fig. 6), together with some accompanying text in pag. 6.
iv)  Since the Universe journal is oriented on publication of the papers related to physics the author has to explore possible astrophysical applications of the obtained results in more concrete way.
As mentioned above, we do not think our paper needs astrophysical justification. But taking into account the view of the referee, we have attempted to connect our study to astrophysics by adding a final sentence in the conclusions.

Reviewer 2 Report

In the present paper the authors discuss various aspects of the \epsilon=+/- scalarization of Reissner-Nordstrom and Kerr-Newman black holes within the framework of  Gauss-Bonnet (GB) gravity. They construct fully non-linear solutions describing static and rotation scalarzied GB black holes with a charge. It is also shown that the well-known analogy between the spinning vacuum Kerr black holes  and the electrically charged static Reissner-Nordstrom solutions can be extended to their scalarized counterparts.  In the last part of the paper, in order to show the general character of their observations, the authors have also considered the scalarization in the presence of dilaton and Yang-Mills fields. 

The paper as a whole is written well and clearly, and contains many new results. In my opinion the results are really interesting and deserve publication.

In conclusion I recommend the paper for publication.      

Author Response

We would like to thank the referee.

Reviewer 3 Report

The paper “Aspects of Gauss-Bonnet (GB) scalarisation of charged black holes”studied the GB scalarisation in various backgrounds of black holes. In particular, the authors studied two types of GB scalarisations, one is GB^+ and the other is GB^-. The author focused much on the solution of the GB^- in the RN and KN black holes, and finally constructed the full nonlinear solutions. This paper is well organized and well written. It contained solid computations, which supports their conclusions strongly. This paper has clarified the problems of GB scalarisation in various black holes, which will surely have some impact on the community.

Therefore, I recommend to accept this paper.

Author Response

We would like to thank the referee.

Round 2

Reviewer 1 Report

Referee report #2
to the revised paper universe-1492786v2 entitled
"Aspects of Gauss-Bonnet scalarisation of charged black
holes"
by Carlos A. R. Herdeiro, Alexandre M. Pombo and Eugen
Radu

The authors of the revised paper universe-1492786v2 have revised the original submission. I conclude that the revised paper is suitable for publication and I recommend to accept it for publication in the UNIVERSE
journal.