Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

  Relationship between Weak Cosmic Censorship and Topological Censorship

+ 10 like - 0 dislike
765 views

The weak cosmic censorship states that any singularity cannot be in the causual past of null infinity (reference).

The topological censorship hypothesis states that in a globally hyperbolic, asymptotically flat spacetime, every causal curve from $J^-$ to $J^+$ is homotopic to a topological trivial curve between the two points. (reference)

I am curious as to the relationship between these two; will a found violation of weak cosmic censorship necessarily mean a violation of topological censorship? [edit: or the converse]

This post has been migrated from (A51.SE)
asked Oct 1, 2011 in Theoretical Physics by Benjamin Horowitz (195 points) [ no revision ]
retagged Apr 19, 2014 by dimension10
BTW, isn't it a bit ironic to cite a paper with the words "Strong cosmic censorship" in the title as your reference to weak cosmic censorship?

This post has been migrated from (A51.SE)
I was originally going to try to make a case relating Strong cosmic censorship to Topological censorship, but I decided I was more interested in weak censorship anyway :P That paper has a concise definition though.

This post has been migrated from (A51.SE)

1 Answer

+ 9 like - 0 dislike

No.

Firstly, weak cosmic censorship can only hold in the generic sense, as there are known examples of nakedly singular space-times. (See, e.g. Christodoulou 1993, and Christodoulou 1999.)

Observe in particular that the nakedly singular space-time constructed in the 1993 paper is spherically symmetric with a central axis, and the initial data is prescribed on a set homeomorphic to $\mathbb{R}^3$. So the maximal globally hyperbolic development of this data, which leads to a naked singularity (hence violating cosmic censorship), is simply connected (homeomorphic to $\mathbb{R}^4$ actually). And hence must satisfy topological censorship.


BTW, if the implication you want were actually true, then given that nakedly singular solutions are known in the literature, it would be rather difficult to have topological censorship be a proven theorem in the generality that it is usually stated.


However, it is interesting to note that the converse (or something quite close to it) of the statement you are interested in actually holds. By a result of Galloway and Woolgar you have that, roughly speaking: weak cosmic censorship + null energy condition implies topological censorship. The contrapositive of which would say that failure of topological censorship + null energy condition holding will imply weak cosmic censorship is false.

This post has been migrated from (A51.SE)
answered Oct 3, 2011 by Willie Wong (580 points) [ no revision ]

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\hbar$ysi$\varnothing$sOverflow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...