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

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

145 submissions , 122 unreviewed
3,930 questions , 1,398 unanswered
4,853 answers , 20,624 comments
1,470 users with positive rep
501 active unimported users
More ...

Einstein's field equation on orbifolds

+ 3 like - 0 dislike
80 views

I was wondering if there is some kind of Einstein's field equation for orbifolds (say semi-Riemannian of Lorentz signature if this make sense).

Here, by an orbifold I mean the "stacky" quotient of, for example, a compact Lie group $G$ acting smoothly on a manifold $M$ and with finite stabilizers...hence the stacky quotient will be (the Morita equivalence class of) its translation (Lie) groupoid $[M\times G\rightrightarrows M]$, in contrast to the "coarse" orbit space $M/G$ which is an object with singularities.

For this kind of stacky objects there is a theory of connections and curvature for $S^1$-bundles (related with Maxwell's equations, I guess)...I´m just curious if there exist more "classical" notions of curvature which allow to state Einstein´s field equation in this context...of course, if this is the case it would be great to think about its meaning from the perspective of singularities as well.


This post imported from StackExchange MathOverflow at 2016-10-07 22:45 (UTC), posted by SE-user Enrique Becerra

asked Sep 23, 2016 in Theoretical Physics by Enrique Becerra (15 points) [ revision history ]
edited Oct 7, 2016 by Dilaton
If by an orbifold you mean a quotient of a, say, lorentzian manifold $(M,g)$ by a discrete group $\Gamma$ acting via isometries, then $M/\Gamma$ with the induced metric is locally isometric to $(M,g)$. So if $(M,g)$ satisfies Einstein's equations, so will the manifold of smooth points on $M/\Gamma$. Is your question then about what happens at the singular locus?

This post imported from StackExchange MathOverflow at 2016-10-07 22:45 (UTC), posted by SE-user José Figueroa-O'Farrill
General Relativity is a mathematical theory developed to model a physical phenomenon (gravity). If you want to ask about what happens at the singular locus, you are in a realm that is already outside the classical domain of GR; so if you want to get a reasonable answer you probably want to say something about what the singular points in your orbifold are supposed to be modelling.

This post imported from StackExchange MathOverflow at 2016-10-07 22:45 (UTC), posted by SE-user Willie Wong
Alternatively, if your interest is purely mathematical, you should say what aspects of Einstein's field equations (or their solutions) you want to reproduce on orbifolds. Then people may be able to come up with viable expressions.

This post imported from StackExchange MathOverflow at 2016-10-07 22:45 (UTC), posted by SE-user Willie Wong

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:
$\varnothing\hbar$ysicsOverflow
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).
To avoid this verification in future, please log in or register.




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

Your rights
...