Jump to content

Talk:Globally hyperbolic manifold

Page contents not supported in other languages.
From Wikipedia, the free encyclopedia

Problem on Spacetimes with Boundary

[edit]

The given definition of global hyperbollicity in reference 1 does not apply correctly to spacetimes with boundary. In this case the condition has to be taken for the interior as a manifold in its own right. Otherwise the existence of a Cauchy surface cannot be guaranteed anymore. One can e.g. cut off a spacetime with non-empty spatial infinity containing a Cauchy surface near spatial infinity. Lets call the result M. Then the timelike spatial boundary of M will be non-empty, which prohibits the existence of a Cauchy surface. The first condition in reference 1 will still be fulfilled as is just replaced by which is compact as the intersection of two compact sets. however will not be compact if . —Preceding unsigned comment added by Doenermaster (talkcontribs) 13:40, 23 October 2010 (UTC)[reply]