Gravitational Radiation at Infinity with Non-Negative Cosmological Constant

Round 1

Reviewer 1 Report

This work deals with the existence of gravitational radiation arriving at null infinity –i.e. escaping from the physical system– is addressed in the presence of a non-negative cosmological constant Λ ≥ 0. The case with vanishing Λ is well understood and relies on the properties of the News tensor field (or the 3 News function) defined. The situation is drastically different when Λ > 0 where there is no known notion of ‘News’ with similar good properties. In this paper both situations are considered jointly from a tidal point of view, that is, taking into account the strength (or energy) of the curvature tensors. My impression is that the paper is technically sound and may have some interest in the wormhole community.

The authors provided a very clear scheme to calculate theoretical models from the perspective of the cosmological constant in this manuscript. The discussion could be interesting and mathematical results could be useful for future related studies.

Thus the subject of the manuscript is certainly of interest to researchers working in relativistic astrophysics and the obtained results could be useful for people interested in the viability of \Lambda. The treatment presented by the authors is rigorous and as far as I can tell, the calculations seem to be correct. I recommend this manuscript for publication as is.

Author Response

Thank you for the report. 

Reviewer 2 Report

This paper provides a useful review of ways to characterize gravitational radiation in spacetimes with \Lambda \geq = 0 that the author and collaborators have obtained. It is overall well written and structured, and would make a good entry point for someone wanting to learn about this subject, so I am happy to recommend it for publication in Universe once some small comments I give below are addressed. Additionally, I have noted some of the typos I noticed, but there are many more—I recommend that this be given a good proofreading before resubmission.

 

L24: It’s probably appropriate to cite a few papers giving the observational evidence for an accelerated expansion of the Universe here.

 

It is not obvious (at least to me) why Eq. (3) follows from the gauge condition, and I don’t see a derivation of this from a quick look at the references given for this.

 

Around Eq. (3), you should probably also specify the covariant derivative \nabla_\mu explicitly (i.e., presumably it is compatible with the g metric, but this should be stated explicitly). It would also be a good idea to introduce the \mathfrak{X} notation, since I was not familiar with it and had to look it up.

 

In Eq. (20), are the R and T indices being summed over (in which case, why not use A and B?), or do they denote specific components?

 

In the equation below Eq. (70), the logic behind the second equality is not clear to me.

 

Below Eq. (76), the argument involving the orthogonality with the conformal Killing vector fields should be expanded on, or a reference given, since this doesn’t seem to follow from previous discussion (or I am overlooking something).

 

In Sec. 6, it would be good to motivate why two copies of \mathcal{F} are appropriate in the expression for X.

 

In Eq. (A16), \omega_B is not yet defined.

 

L560: It’s probably a good idea to give a reference for the uniqueness statement, as in Ref. [53].

 

It’s probably a good idea to state that the equation below Eq. (A24) is the trace of Eq. (A22), as in Ref. [53].

 

The statement of Lemma A3 should specify what \zeta is.

 

* Minor:

 

L25: “be” is missing after “might”

 

L64: Need to start a new sentence with “Furthermore” (it’s currently a comma splice)

 

L65: “Hence” should be capitalized

 

L68: | should be \ to get the symbol.

 

Below Eq. (2), “concorde” -> “concord”

 

L86: “Minskowskian” -> “Minkowskian”

 

Above Eq. (9), “concentrate in the physical relevant case” -> “concentrate on the physically relevant case”

 

In the second expression in the equation below Eq. (16), c is used as both a free and dummy index.

 

Below Eq. (44), “Caley” -> “Cayley”

 

Above Eq. (65), “by” -> “be”

 

Two lines below line 484: “filed” -> “field”

 

In Appendix B, the subscript “round” should be set in Roman.

 

Is there any reason to have the vector arrow on \zeta in the Lie derivative in Eq. (A24), but not for \chi in Eq. (A23) or in the Lie derivatives in other places, e.g., Eq. (14)? I think that the version without the vector arrow is cleaner.

Author Response

Many thanks for a detailed and useful report. I have followed all the recommendations, clarified the points raised, and added the needed references. I have also added some new material and thoroughly proof-read the paper, that was plagued with typos.

Reviewer 3 Report

The author found a new geometric interpretation of the news tensor for spacetimes with a vanishing cosmological constant. Based on this new observation, the author proposed a novel approach to characterize the gravitational radiation in spacetimes with a non-negative cosmological constant.

In the case of a vanishing cosmological constant, the situation is well-understood, and the news tensor fully captures the information of gravitational radiation. However, the issue of a positive cosmological constant remains unsolved despite much recent progress. 

The author provided a comprehensive review of the background and recent development of the subject, and the proposal for the new case is clearly written. 

To summarize, the manuscript provides important insight into a fundamental and longstanding problem in gravitational radiation.

However, I recommend thoroughly editing the manuscript before considering it for publication. Below is a list of corrections I suggest (up to line 60 of the manuscript)

Line 7  syper-momentum to super-momentum

Line 25 This constant might be an effective one, or a true new universal constant 

Line 38 balck hole to black hole

line 47 asypmtotic symmetries to asymptotic symmetries

line 51 a basic problems to a basic problem

line 52 funsamental to fundamental 

line 58 the the Bel-Robinson tensor to  the Bel-Robinson tensor

 

 

 

 

Author Response

Thanks for the report and the corrections. I have added some new material and references. And I have proof-read and edited the manuscript that, unfortunately, was plagued with typos.