De Sitter-Invariant Black Holes
Round 1
Reviewer 1 Report
Please find the report in the attachment.
Comments for author File: 
Comments.pdf
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 2 Report
The paper brings a proposal for new physics based on the de-Sitter invariant approach, presenting a black hole solution reflecting solution of the Modified Einstein equations of the "vacuum type", with vanishing right hand side of the Einstein equations. In the presented model the currents of energy-momentum of matter and the proper conformal current related to the de Sitter symmetries are connected internally. The authors have to address several points before the paper could be published.
1. The de-Sitter invariant BH is defined as so caled "vacuum solution" with vanishing of the whole right hand side of the modified Einstein equations, i.e., it is assumed that the mass current and proper conformal current calcel each other. However, in the quantum physics the vacuum correspond to vanishing of the stress energy of the mass. Morever, J. Zeldovich have demonstrated that the vacuum stress-enegy tensor corresponds to the cosmological constant in the standard Einstein theory. Therefore, what is the approach to the quantum mechanics (QM) and vacuum definition in the new framework? What is the role of the standard QM vacuum in the new theory, or what is the role of the inflationary inflaton fields in the new framework, as in the new framework the mass and the de-Sitter proper conformal currents are dynamically connected?
2. How to undestand the two differing definitions of the BH solutions? It seems that it is more convenient to say that the r_M=2M and the r_{\Lambda}=l^2/M are two distance scales interconnected by the mass parameter M, and use only the standard definition of the BH horizon.
3. The definition of the energy (density) in Eq.68 means that the difference of the energy and proper conformal energy must be constant in dynamical situations. However, what is the stability of the system under perturbations?
4. How can we treat the collective phenomena having two or several BHs when gravitational waves have to be emitted due to their interactions?
5. How the cosmic (collective) cosmological constant is defined in the case of many-BH system, if each of them has different mass and de-Sitter scale? What is the case of "non-vacuum" solutions?
6. What is the stability to the rotational perturbations? The rotation of the matter object have to destroy the de-Sitter invariance, breaking the basic assumption of the framework. Could you apply in such situations something like invariance to the Godel Universe? Or it means some breaking of symmetry in the sence of gauge field?
7. How the cosmological models will be constructed in the presented framework?
8. The comparison with the non-standard approaches to the standard cosmological constant in the standard Einstein theory should be presented, namely for evolving cosmological constants. Also comparison to the old idea of A.D.Sakharov of dynamical cosmological constant representing elasticity of evolving spacetime could be done.
9. The motion of test particles should be mentioned, especially in connection to the possible existence of the so called static (turnaround) radius playing a crucial role in astrophysical processes around standard SdS or KdS spacetimes, discussed e.g. in PRD 60, 044006 (1999), JCAP 10, 013 (2015), Universe 6, 26 (2020).
The English should be improved, some misprints have to be corrected.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
I am very sorry, but I decided to propose to reject the paper at the present state. The reason is rather paradoxical -- I consider the paper to be very interesting and I like very much the basic idea. For this reason I propose to modify the paper in order to make it much stronger by clearing up some details and cancelling some very weak points, as accepted by the authors in their response to the criticism. I would like to give a guide for the modified version.
1. The authors have to discuss in more detail the most crucial basic poit of their approach, namely the fact that matter is determining the basic de Sitter geometry, its its parameter Lambda, in the SdS geometry representing the vacuum case, and the representation of this connection in non-vacuum spacetimes.
2. To make clearer the terminology of two kinds of horizons that is rather misleading.
3. Express in more detail the possible reaction of the accretion of matter when the basic assumption of the SdS solution is violated.
4. Give some characteristics of possible accretion of matter.
5. Make a clear statement of the open question of relation of local dS spacetimes, and the global influence of an averaged "cosmological term" in the framework of cosmological models.
Minor editing of English language required.
Author Response
Please see the attachment
Author Response File: Author Response.pdf
Round 3
Reviewer 2 Report
The paper can be published in its present form.
No comment
