# Cosmic Censorship of Trans-Planckian Field Ranges in Gravitational Collapse

### Submission summary

 As Contributors: Chethan Krishnan Arxiv Link: https://arxiv.org/abs/2003.05488v2 (pdf) Date submitted: 2020-07-18 02:00 Submitted by: Krishnan, Chethan Submitted to: SciPost Physics Academic field: Physics Specialties: High-Energy Physics - Theory Approach: Theoretical

### Abstract

A classical solution where the (scalar) field value moves by an ${\cal O}(1)$ range in Planck units is believed to signal the breakdown of Effective Field Theory (EFT). One heuristic argument for this is that such a field will have enough energy to be inside its own Schwarzschild radius, and will result in collapse. In this paper, we consider an inverse problem: what kind of field ranges arise during the gravitational collapse of a classical field? Despite the fact that collapse has been studied for almost a hundred years, most of the discussion is phrased in terms of fluid stress tensors, and not fields. An exception is the scalar collapse made famous by Choptuik. We re-consider Choptuik-like systems, but with the emphasis now on the evolution of the scalar. We give strong evidence that generic spherically symmetric collapse of a massless scalar field leads to super-Planckian field movement. But we also note that in every such supercritical collapse scenario, the large field range is hidden behind an apparent horizon. We also discuss how the familiar perfect fluid models for collapse like Oppenheimer-Snyder and Vaidya should be viewed in light of our results.

###### Current status:
Has been resubmitted

We thank the referee for the review. But unfortunately, despite his/her kind recommendation to accept with minor changes, we have made some substantive changes in the paper, including a change of title -- https://arxiv.org/abs/2003.05488

A key point is that at late times, there are two solutions to the apparent horizon equation and only the smaller one is inside the region of interest. Since the time of submission of the original version, we have noticed that in EVERY single case that is not too close to criticality, a bigger (and therefore correct) solution forms just outside, to cover up the large field range! This is a very strong suggestion that there is a cosmic censorship like mechanism in effect during gravitational collapse, that censors large field ranges.

While this result is quite interesting, it is a sharp deviation from our original punchline. While our original numerical results for the evolution are still correct, the interpretation changes completely.

We believe this also addresses the referee's query in the second paragraph - note that it is not very easy to construct Penrose diagrams of numerical gravity solutions, so we don't have a direct answer to his/her question. But the statements we have made above about the apparent horizon, together with the fact that the apparent horizons are expected to be inside global event horizons lead to a new observation -- trans-Planckian field ranges during collapse are always censored by a horizon.

So the main results of the paper are now -- (a) gravitational collapse of fields GENERICALLY lead to super-planckian field ranges, and (b) these field ranges are are always hidden behind apparent horizons.

The tension with the firewall is also gone.

### List of changes

We have changed the title, a crucial sentence in the abstract, and removed/changed some paragraphs in the intro and conclusion to reflect our new perspective. We have also added a small section on the determination of apparent horizon, since it has turned out to be a more subtle and important issue than we expected.

### Submission & Refereeing History

Resubmission 2003.05488v3 on 11 August 2020

Resubmission 2003.05488v2 on 18 July 2020
Submission 2003.05488v1 on 31 March 2020

## Reports on this Submission

### Anonymous Report 2 on 2020-8-9 Contributed Report

• Cite as: Anonymous, Report on arXiv:2003.05488v2, delivered 2020-08-09, doi: 10.21468/SciPost.Report.1905

### Strengths

This is a very clear paper on an interesting and timely topic. It provides convincing numerical evidence that scalar field collapse probes super-Planckian field values, but that these values are hidden behind a horizon. It is well-written, informative and a pleasure to read.

### Weaknesses

There are a few minor issues.

1. The Swampland Distance Conjecture refers to the distance in scalar field space, not just the field value (which is not reparametrization invariant). It would be useful to emphasize that for the theory studied in this paper, the scalar field value is the same as the distance in field space, so the discussion really is phrased in terms of a physical, invariant quantity. For instance, the first bulleted concern in the Discussions asks about coordinate choices, but this concern applies to coordinates on field space as well as on spacetime.

2. The discussion of the relationship to other work on super-Planckian spatial variations of fields could be improved. The authors mention a "Heuristic Black Hole Argument" and cite a 2008 paper of Nicolis, but they also say this is "usually attributed to T. Banks." I don't think that this attribution is quite correct. Banks discusses this at the beginning of section 3 of arXiv:1910.12817, where he says that "it was pointed out" to him at a Rutgers group meeting; unfortunately, he doesn't say who pointed it out. If there is something to cite before the paper of Nicolis, perhaps it is the related paper by Banks, hep-th/0011255, but it does not contain quite the same claims. Another, more tangentially related, early paper is arXiv:0705.2768 by Arkani-Hamed, Orgera, and Polchinski, which finds super-Planckian variations in some axionic wormhole solutions. (Although it predates the Nicolis paper, it mentions the basic "Heuristic Black Hole Argument" as if it was a well-known fact at the time.)

More recently, there have been a few papers that explore how large spatial variations of fields might be censored. One of these is cited as Ref. [8] (by Klaewer and Palti), but in the context of a list of references to the Swampland Distance Conjecture. I think it should be singled out as being closer to the topic of the current paper than the other SDC references. Similarly, arXiv:1701.05572 by Dolan, Draper, Kozaczuk, and Patel studies large spatial variations of axion fields around strings; arXiv:1901.00515 by Draper and Farkas studies large spatial variations of scalar fields in Kaluza-Klein bubble geometries; and arXiv:1910.04804 continues this study. The latter reference makes a conjecture about censorship of super-Planckian spatial field excursions, namely that they are bounded by $|\log(R \Lambda)|$, with $R$ the size of the spatial region over which the field varies and $\Lambda$ a UV cutoff on the theory. (This is consistent with examples of arbitrarily large field variations that are not screened by horizons, but arise only in tiny regions of space.)

I think that the introduction to this paper, and the paragraph in the conclusions that "raises the speculative possibility" that horizons hide large field variations, should refer to this existing body of literature. (In particular, there are known examples where the variations are not hidden behind horizons.)

3. Reference [21] should supply an author and title, not just a web address.

### Report

This paper should be published, after minor revisions to address the small issues noted under "Weaknesses." It is a high-quality paper that clearly meets the publication criteria of SciPost. It makes an interesting contribution to the field, in an area that many people are actively working on, and it does so in a concise, clear, convincing way.

### Requested changes

See under "Weaknesses."

• validity: top
• significance: high
• originality: high
• clarity: top
• formatting: excellent
• grammar: excellent

### Anonymous Report 1 on 2020-7-26 Invited Report

• Cite as: Anonymous, Report on arXiv:2003.05488v2, delivered 2020-07-26, doi: 10.21468/SciPost.Report.1862

### Report

In the new version of the manuscript submitted by the authors, they have argued that the gravitational solutions they found for scalar collapse always have an apparent horizon which hides the large field displacements behind it. This sufficiently addresses my question about the location of the region of large field displacement relative to the horizon of the incipient black hole, and also resolves the purported tension with the validity of EFT at the horizon in the previous version. As I stated in my previous report, the paper is clear, well-written, and the results are definitely of interest to the broad high energy theory community. I recommend publication of the paper without further changes.

• validity: -
• significance: -
• originality: -
• clarity: -
• formatting: -
• grammar: -