Dynamical Black Holes and Accretion-Induced Backreaction

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript presents a new perturbative method incorporating time dependence into evaluations of the locations of spherical black hole horizons.  The appears to be of good quality and should be published.  There are, however, a few ways in which the presentation could definitely be improved.

I do not think that the characterization of the metric as having a "Vaidya-dark energy form" in the vicinity of a horizon is particularly useful, and it may actually be somewhat misleading.  In fact, it should actually be true that any non-vacuum solution of the Einstein field equations may be written in a similar form locally.  Over a small spacetime distance scale, over which the stress-energy-momentum tensor T does not vary appreciably, one may always approximate the tensor as being constant; then its trace component may be identified as a contribution that looks equivalent to a cosmological constant term in that vicinity.  However, when this equivalence is strictly local and when the trace is not the only term in T, this characterization does not seem to be illuminating.  So I advise the authors against using this description of the local character of the stress-energy-momentum tensor near a horizon.

Since the discussion of trapping horizons is deferred to the appendix, I was a bit surprised that the details of their meaning was not spelled out in greater detail.  Line 392 begins, "By definition, there is a trapping horizon...," without reference to where this definition comes from.  The meanings of horizons of various types can be complicated, and nowhere in the current manuscript do I find a clear statement of precisely what the authors' definition of a trapping horizon entails.  It would make things quite a bit easier for readers to have that information prominently presented, preferably in the introduction when trapping horizons are first mentioned as part of a quasi-local approach to characterizing black holes, or perhaps around line 118 where they are mentioned again.  [In a similar vein, the (Lie?) derivatives appearing in eqs. (A9–A10) are never fully defined.]

It would be nice to have a brief discussion, around eq. (50) in section 4.2, of to what extent an initially Reissner-Nordström black hole may be extremal if it has been accreting mass.  After all, the extremal Reissner-Nordström solution is characterized by having the entire ADM mass be associated with its charge Q.  So does accretion onto a Reissner-Nordström black hole automatically break extremality, but adding (non-charge) mass energy?

There are also a few minor composition errors that need correction:

At line 109, there is a "FOTH" where it should say "FITH".

At line 136, the authors use "revised" where "reviewed" is meant; the two words are not synonyms in English.

In lines 157–158, the text states:  "Such cases raise profound theoretical challenges, including potential violations of the cosmic censorship conjecture...."  This should be rephrased, since a naked singularity is essentially the definition of a violation of the cosmic censorship "conjecture"—and I put "conjecture" in quotes, because it is already known not to hold universally in general relativity.

The sentence, "Some key advances of our perturbative approach are commented," at line 292 is not idiomatic and should be rewritten.

The use of a capital M on the right-hand-side of eq. (60) does not match previous notation [such as eq. (45)].

Author Response

 

Dear Reviewer 1,

Thank you for your feedback. We have carefully considered all your comments and have revised the manuscript accordingly. The detailed responses to each of your suggestions are provided in the attached file (Response_Reviewer1.pdf), and the corresponding changes have been incorporated into the updated version of the manuscript.

We sincerely appreciate the time and effort you have dedicated to reviewing our work. Your insights have improved the quality of the paper. 

Best regards,
The Authors

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Dear authors,

I read with great interest your work "Dynamical black holes and accretion-induced backreaction", showing an analysis of dynamical trapping horizons in spherically symmetric spacetimes using the Misner-Sharp mass framework and ingoing Eddington-Finkelstein coordinates.  A near-horizon perturbative scheme is introduced to study the backreaction of accreting matter on black-hole geometries, culminating in applications to Reissner-Nordström (RN) black holes, including extremal and near-extremal configurations. The authors show that momentum influx and energy density affect the location and structure of horizons in distinct ways. Furthermore, repulsive corrections to the metric are analyzed as a mechanism to eliminate inner (future inner trapping) horizons. Nevertheless, I have some comments and questions, implying revisions to your work:

(i) Please, along with the document is always well recommended to explain all the acronyms (for example, on page 1 (ADM)Arnowitt, Deser, and Misner, etc.).

(ii) On page 1, line 21, you wrote: " beyond traditional tools like event horizons and ADM/Komar mass". Where is the reference about it?

(iii) From eq. (15), page (4), you consider a generalized first law of black-hole thermodynamics, with ingredients given by the area and volume. There exists a relation between this law and the classical thermodynamical results in black hole thermodynamics (for example, connecting the surface gravity with the Hawking temperature). ?

(iii) On page 6, in eq. (24) you wrote: " This result implies that the metric can be approximated to a“Vaidya-dark energy form”around r0 with an effective dynamical cosmological constant..." Please, explain more about this. Is the effective $\tilde{\Lambda}$ fully equivalent to a variable cosmological term? 

(iv) On subsection 4.1, the perturbative control parameters should be more explicitly stated. At what threshold do second-order corrections become non-negligible?

(v) On page 11, section 5, in eq. 59 the authors propose to include the term αr^−β in the Misner-Sharp mass. It recalls corrections from quantum gravity or effective field theory. However, the origin of these corrections remains speculative. A more detailed justification from either a semi-classical model or a known effective action (e.g., loop quantum gravity, non-local gravity) would improve the physical grounding. I would be well to justify this part with more detail.

(vi) Following the above, the statement that you write between lines 314 and 315 ("...We have observed that the smaller the FITH is, the easier it is to destroy..."), should be interpreted cautiously. What are the causal or thermodynamic consequences of such removal?

(vii) In Section 6, Final Remarks. Open problems where the authors can explore?

 

Author Response

 

Dear Reviewer 2,

Thank you for your feedback. We have carefully considered all your comments and have revised the manuscript accordingly. The detailed responses to each of your suggestions are provided in the attached file (Response_Reviewer2.pdf), and the corresponding changes have been incorporated into the updated version of the manuscript.

We sincerely appreciate the time and effort you have dedicated to reviewing our work. Your insights have improved the quality of the paper. 

Best regards,
The Authors

 

Author Response File: Author Response.pdf