Generalized Darmois–Israel Junction Conditions

Round 1

Reviewer 1 Report

The paper used the limit of a sequence of classical functions to represent the Delta function and formulated a regularization procedure with this method to handle singularities. The results of junction conditions in quadratic gravity can reduce to known results for the Gauss-Bonnet theory. The paper is well presented and I recommend it to be accepted for publication.

Author Response

We thank the referee for his comments.

Reviewer 2 Report

In the manuscript “Generalised Darmois-Israel Junction Conditions” the authors address the question of defining junction conditions for F(R), and  quadratic modified gravity theories.  The authors point out that the previous works on this subject have somewhat  underestimated the contribution of terms involving the products of the Heaviside step function, which characterise the approach to the interface between solutions from both sides.

In the present manuscript the authors present a more general procedure by integrating the bulk equations of motion  across the infinitesimal width of the singular surface in the spirit of the central work of Israel.

The manuscript is rather long, but it is very well written, and provides the reader with a thourough idea of the cross-relation between the authors’ work and previous contributions  on the same subject. In particular it renders clear to which extent the methodology adopted by the authors, overcomes the limitations of previous works. It also addresses how the approach adopted in the manuscript relates to the Hadamard regularization, providing a consistency interpretation. This is, in the suite, strengthened by  showing that one  recovers the Gauss-Bonnet theory when applying the authors’ procedure to the  gravity theory endowed with quadratic terms in the fundamental action.

Moreover, the work offers  further illustrations of how the procedures apply to concrete problems, ranging form the F(R) higher-order gravity theory to the low-energy limit of the Heterotic String, to thin-shell wormholes in R-squared gravity, and finally to stellar models.

The results of the manuscript seem sound to me, and are a relevant contribution for the important subject of sewing two different solutions/spacetimes at junctions. The fact that  this is done for generalised  gravity theories that have attracted a considerable interest during the last decades in the quest for an explanation for the late inflationary stage of the universe  makes the present work of great interest. 

Thus I recommend the publication of the present manuscript in the journal Universe.

As a final remark, I do not have any changes to suggest, and I only spotted two typos: in eq. (2.7) the index ’n’ should presumably be contra-variant in the  first equality; in the line before Eq. (4.5) it should be “The equations… read” rather than “reads”.   

Author Response

We thank the referee for his comments. We have corrected the typos in the revised version of the manuscript.