Closed Timelike Curves, Singularities and Causality: A Survey from Gödel to Chronological Protection

Round 1

Reviewer 1 Report

Please find the attached pdf file Report_Universe_1041888 that contains my report.

Comments for author File: Comments.pdf

Author Response

I thank the referee for his comments and suggestions of additional references. While he did not sign his review report, I could easily recognize my friend and colleague  Marcelo Rebouças, because he contributed a lot to the field of Closed Timelike Curves (CTCs), and he is an author of most of the additional references he suggests !

Of course I knew that the topic of CTCs had been dealt with in hundreds of articles and books, so that I could not be exhaustive and in my review I tried to make a short and rather balanced selection. It's the reason why, in my original manuscript, I didn't quote more than 2 papers by Rebouças and collaborators. Now, since, acting as the referee, M.R. considers that in order to be published my review requires a major revision by including more references, I followed his advice in the revised manuscript. 

More precisely:

• I revised section 2 in order to include all the comments and references suggested by the referee in points 1 & 2.
• In section 3 dealing with Singularities, I included additional references to Penrose, Raychaudhuri, etc. and I reformulated the brief history of singularity theorems.      
• In section 4 I included the remarks of the referee concerning the "self-consistency principle" and I add references he suggested in his points 4 and 5.
• I checked the misprints/mistypes in the list of references
• By doing this I consider that I fully satisfied the requests of the referee.        

Reviewer 2 Report

The author reviews the field of closed time-like curves. After a historical survey he discusses some of the outstanding issues surrounding the existence or not of CTCs, particularly highlighting the relationship between singularities and CTCs and attempts to find physical mechanisms for "chronology protection". He finishes by discussing in a bit more detail one possible method for excluding CTCs by building in causality from "the ground up", that is CDT theory.

I found the presentation accessible, interesting and informative and delivered in an even-handed way. The field is large so inevitably there are gaps (particularly in terms of possible quantum mechanisms for resolving the causal paradoxes implied by CTCs), but the author does a good job of discussing the main issues and highlights interesting points. The mathematical details are only alluded to, but there is sufficient referencing such that the interested reader can follow up the details.

I think this is a useful short review. I am happy to recommend publication.

Author Response

I thank the anonymous referee for his positive report, which does not require revision of my text

Reviewer 3 Report

The problem of causality is one of the most interesting and controversial problems of the quantum field theory. One of the most attracting situations which probably could lead to possible causality violations is the problem of closed timelike curves arising within certain solutions of general relativity.

The present paper gives an excellent pedagogical review to a problem of causality within gravity context. This problem is illustrated by analogies with science fiction literature.

It is explained how the causality breaking arose within the gravity context, where the first non-causal solution has been presented by Gödel in 1949, being motivated by preliminary studies of rotating metrics, and further, various developments of this metric and other causality-breaking metrics were proposed. An excellent review of such solutions including wormholes, Misner and Alcubierre solutions is given.

At the same time, causality is treated as a fundamental physical principle being confirmed both by logical reasons and physical observations. Therefore, the problem established in the paper is -- whether there is any mechanism within gravity theory allowing to rule out causality breaking? It is argued in this paper that one of the best manners to do it is based on the causal dynamical triangulations. An introduction to this concept is given.

By my opinion, this paper represents itself as an excellent review on causality problem in gravity and hence can be published in its present form.

Author Response

I thank the anonymous referee for his very positive report, which does not require revision of my text

Round 2

Reviewer 1 Report

I am happy that my friend and colleague Jean-Pierre Luminet dealt satisfactorily with the points and suggestions of my report. I hope they motivate improvements of his review article.  I recommend the publication of his nice and motivating paper.   

Please note that I did sign my report, but an 'Universe' rule is that  "the authors will not know your identity until the paper is published". 

I final minor point: my friend and colleague from Stockholm, J. E. Aman,  is co-author of ref.[18]

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.