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Massive scalar clouds and black hole spacetimes in GaussBonnet gravity
by Iris van Gemeren, Tanja Hinderer, Stefan Vandoren
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Submission summary
Authors (as registered SciPost users):  Iris van Gemeren 
Submission information  

Preprint Link:  https://arxiv.org/abs/2405.13737v2 (pdf) 
Date accepted:  20241015 
Date submitted:  20241003 17:55 
Submitted by:  van Gemeren, Iris 
Submitted to:  SciPost Physics Core 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approaches:  Theoretical, Phenomenological 
Abstract
We study static black holes in scalarGaussBonnet (sGB) gravity with a massive scalar field as an example of higher curvature gravity. The scalar mass introduces an additional scale and leads to a strong suppression of the scalar field beyond its Compton wavelength. We numerically compute sGB black hole spacetimes and scalar configurations and also compare with perturbative results for small couplings, where we focus on a dilatonic coupling function. We analyze the constraints on the parameters from requiring the curvature singularity to be located inside the black hole horizon $r_h$ and the relation to the regularity condition for the scalar field. For scalar field masses $m r_h \gtrsim 10^{1}$, this leads to a new and currently most stringent bound on sGB coupling constant $\alpha$ of $\alpha/r_h^2 \sim 10^{1}$ in the context of stellar mass black holes. Lastly, we look at several properties of the black hole configurations relevant for further work on observational consequences, including the scalar monopole charge, Arnowitt Deser Misner mass, curvature invariants and the frequencies of the innermost stable circular orbit and light ring.
Author comments upon resubmission
List of changes
List of changes
 We broadened the citations on the current constraints on the coupling constant, as suggested by point 1) of the referee. This is changed in the last paragraph of section 2.1
 We added a few sentences on the explanation for the choice of the exponent in the coupling function in the first paragraph of section 5 as suggested by the referee point 6).
 Based on suggestion 2) of the referee, we changed the statement “we conclude that the perturbative solution also becomes more accurate in the large scalar mass regime” in section 5.1.3 to “Together with this analysis we conclude that the perturbative solution deviates less from the exact solution in the large scalar mass regime. As expected as for large scalar masses the scalar field decreases and decouples in the limit of the mass to infinity.”
 We added a new section 5.2 discussing the results on the horizon radius as function of the black hole mass shown in new Fig. 5 as suggested by point 3) of the referee. This diagram and analysis complements Fig. 5 of 1903.08119 containing similar diagram, as we show the effect of the scalar field mass and coupling constant on the horizon radius independently, whereas in the aforementioned work focussed on the dependence of the combined parameter from the mass and coupling. We shortly refer back to the results in this section in our discussion on the theoretical bound on the coupling constant at the end of section 6.2. Our main conclusions stay unaltered.
 We changed section 6.2 according to suggestions 4) and 5) of the referee. At the end of the first paragraph we elaborated on the explanation why we assume the scalar field solution to be monotonically decreasing also in the general coupling case. To improve the clearity of the rest of this section, we added bullet points to describe what is shown in the left panel of Fig. 8. To make the argument and procedure of how the right panels of the original Fig.7 are produced better readable, we decided to only keep the bottom panel on the maximum coupling in the main discussion. As the cusp feature is already visible in the left panel and our main discussion on comparing to two types of constraints is also captured by showing only the bottom right panel. The top right panel of the maximum $phi_h$ is now placed in an additional appendix E with a step by step description on how the values of $alpha_max$ and $phi_h$ max are obtained.
 To increase the readability of section 6.2.1 pointed out by suggestion 7) of the referee, we elaborated on how we did the comparison of the observational constraint on the coupling versus our result of the theoretical bound on the coupling in Fig. 7) in a step by step manner, explicitly writing down the equation to rewrite the mass from dimensionless to the dimensionfull case. The contents of this section remains unaltered.
 Our final conclusions remain unaltered, we only rephrased the sentences related to section 6.2 to only focus on the diagram showing the maximum coupling constant in Fig.7 as the maximum $phi_h$ diagram is now replaced in the new appendix E.
Minor alterations:
 We wrongly referred to the multi panel figures as having top and bottom panels while they are horizontally placed, we changed this referring to left and right panels.
 The numbering of equations in the appendix still had normal counting, we changed this to numbering according to the appendix label, e.g. (A.1).
Published as SciPost Phys. Core 7, 069 (2024)
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The authors have made an effort to improve their manuscript. They have addressed all my comments. So I can recommend it for publication in its present form.
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