The Distributional Stress–Energy Quadrupole and Gravitational Waves

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this self declared review paper, the authors discuss the distributional stress-energy quadrupole in the context of gravitational waves. First, they compare and contrast the Dixon and the Ellis representations for quadrupoles. Then they explain how distributional stress-energy quadrupoles act as sources of gravitational waves and present their results. There are few small issues as in line 22 where the term PDE is not defined. Figure 1 is not called in the text. In line 63 "de Rham pushforward"  needs a reference. In line 73 the reference 8 is out of order. There is a square in line 93 and 95, with no meaning. In section 4 there is a lack of meaning in the second line. In lines 160 and 168, the two references are the same. These are small issues, but for a review paper there should be more explanation in the passages from one equation to another, for example 5.2 introduces a connection as used in one of the references, in the connections appears a upper index M, and the same in the previous line appears a upper index m that have no explanation in the text. As a review paper the passages and terms should be better explained, the paper is too short for it, also there references section is kind of short. For a normal paper it will be ok but not for a review. Attached is a file with the same comments highlighted in the text.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

There is few issues, for example the second line is section 4, maybe there are two periods missing. 

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

In this review, the authors explore the formalism of stress-energy quadrupole regarding its role as the source of gravitational waves.
The Schwartz distributional stress-energy quadrupole can be interpreted as a source of gravitational waves.
The quadrupole distribution is well-defined up to several constitutive relations.

The authors compared the Dixon and Ellis representations for quadrupoles.
The tensorial equation for the components and the constraints are given.
Subsequently, the authors elaborate on how distributional stress-energy quadrupoles serve as the source of gravitational waves.
This leads to an explicit formula for the linearised gravity in the case of a background Minkowski space.
The number of free components for a stress-energy quadrupole is determined.
Moreover, the authors compared their results with other approaches in the literature.

The paper is well-written, and the topic is relevant to the area.
Therefore, based on the above considerations, I recommend its publication in Universe.

Comments on the Quality of English Language

In general, the paper is well-written.

Author Response

We thank the referee for their positive comments. We have asked an English speaker to check the new version of the manuscript.

Please also see the attachment for response to other referee and academic editor.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The work is much better after the revision, There are some places were there is the use of fig. other times the use of figure.  The references not in order along the text, but this is a review for the Journal. Scientifically the paper is sound.

Comments on the Quality of English Language

The English is fine for me, a native speaker could find some problems. But I think is normal for the Journal to make a English review. 

Author Response

We thank the referee for their suggestions. We have changed all the references to figures to Fig. and have made sure the bibliography is in the correct order.

 

Thank you.

Yours sincerely
Jonathan Gratus and Spyridon Talaganis