Need Help Understanding Misner Space Terminology

[Quantum Copy]

Hello! I'm having trouble understanding some of the terminology used to describe Misner (or Milne) Space. Some of the words that are troubling me are "Orbifold" (is this related at all to the cylindrical structure of the Misner universe?), "translation symmetry" (does this refer to the idea that the opposite "walls" of this space-time are identified with each other, so that if you enter one wall you emerge from the opposite one?), "axisymmetric Bianchi I universe" and "Klein bottle topology". I'm trying to understand more about Misner space, because I find it to be such a fascinating model, but I need some help with the terminology. Thanks so much!

 

[tiny-tim]

Welcome to PF!

Hi Quantum Copy! Welcome to PF!

Some of the words that are troubling me are "Orbifold" (is this related at all to the cylindrical structure of the Misner universe?), "translation symmetry" (does this refer to the idea that the opposite "walls" of this space-time are identified with each other, so that if you enter one wall you emerge from the opposite one?), "axisymmetric Bianchi I universe" and "Klein bottle topology". I'm trying to understand more about Misner space, because I find it to be such a fascinating model, but I need some help with the terminology. Thanks so much!

"Orbifold" and "Bianchi I universe" … dunno.

"translation symmetry" … no, it just means it looks the same everywhere … see http://en.wikipedia.org/wiki/Translational_symmetry

"Klein bottle topology" … look at the "Construction" section of http://en.wikipedia.org/wiki/Klein_bottle