Understanding AdS Global Hyperbolicity: Insights from Hawking and Ellis

  • Context: Graduate 
  • Thread starter Thread starter LAHLH
  • Start date Start date
  • Tags Tags
    Hyperbolic
Click For Summary
SUMMARY

The discussion centers on the global hyperbolicity of Anti-de Sitter (AdS) spaces, referencing the work of Hawking and Ellis. Participants explore the implications of closed time-like curves in AdS spaces, noting that such curves prevent global hyperbolicity. The conversation highlights the utility of Penrose diagrams for visualizing these concepts and emphasizes the finite return of objects, like stones, thrown in AdS space. Understanding these principles is crucial for grasping the complexities of spacetime in general relativity.

PREREQUISITES
  • Familiarity with Anti-de Sitter (AdS) spaces
  • Understanding of closed time-like curves
  • Knowledge of global hyperbolicity in general relativity
  • Ability to interpret Penrose diagrams
NEXT STEPS
  • Study the implications of closed time-like curves in general relativity
  • Learn about Penrose diagrams and their applications in spacetime visualization
  • Investigate the concepts of global hyperbolicity and its significance in AdS spaces
  • Review the foundational work of Hawking and Ellis on spacetime geometry
USEFUL FOR

Physicists, mathematicians, and students of general relativity seeking to deepen their understanding of spacetime structures, particularly in the context of Anti-de Sitter spaces and their properties.

LAHLH
Messages
405
Reaction score
2
Is there an easy way to see this? can it be see via the penrose diagram? does it have anything to do with how when a stone is thrown in AdS it will alwayscome backk in finite time..
 
Physics news on Phys.org
I'm not familiar with AdS spaces, but according to the Wikipedia page, it says that these spaces have closed time-like curves. Any manifold with closed time-like curves cannot be globally hyperbolic.
 
Have a look at Hawking and Ellis.
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
1K
  • · Replies 18 ·
Replies
18
Views
4K
  • · Replies 7 ·
Replies
7
Views
4K
  • · Replies 14 ·
Replies
14
Views
5K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 26 ·
Replies
26
Views
3K
Replies
9
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 16 ·
Replies
16
Views
4K
  • · Replies 10 ·
Replies
10
Views
2K