# Compactly generated vs. compactly constructed causality violating region?

+ 2 like - 0 dislike
74 views

I am currently trying to grasp the nuance between a compactly generated future Cauchy horizon (as per Hawking's chronological protection conjecture) and a compactly constructed causality violating region (as per Ori's spacetime).

From what I understand, a compactly generated one is just when the past geodesics of the region lead back to a compact region in some achronal spacelike hyperslice. So if we have some big partial Cauchy surface $S$, something of the form $J^-(H^+(S)) \cap S$ being compact. Basically the creation of the chronology violating region stems from finite region of space.

On the other hand, compactly constructed causality violating region seem to be defined by $\overline{D^+(U)}\cap \mathcal{V}(M) \neq \varnothing$, with $U$ some compact subset of $S$ and $\mathcal{V}(M)$ the causality violating region. So there are CTCs in the closure of the Cauchy horizon (so equivalently I suppose, $H^+(U) \cap \mathcal{V}(M) \neq \varnothing$). The definition comes from "Geometric analysis of Ori-type spacetimes" as the concept doesn't seem to be written down in Ori's papers.

While I can appreciate that their definitions are different, I am having a hard time grasping how a compactly constructed CTC isn't also compactly generated. Ori does go on to say that

"We emphasize again that although probably not ”compactly generated”, our model does demonstrate the formation of closed causal loops from the initial data on a compact vacuum region $S_0$."

This paper also mentions :

"How can this spacetime evade the theorems of Tipler and Hawking? The answer is that N is not in fact the fountain where the causality violating region originates, but rather a place where the Cauchy horizon terminates. The origin of the causality violation lies outside the region where the weak energy condition is obeyed."

So I am not sure exactly what is going on there and where the subtelty lies between the two.

This post imported from StackExchange Physics at 2015-07-21 12:31 (UTC), posted by SE-user Slereah
 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): Email me at this address if my answer is selected or commented on: 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$\hbar$ys$\varnothing$csOverflowThen 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.