Does anyone know asymmetric dynamic global solutions to Einstein eqs?

Click For Summary
SUMMARY

This discussion centers on the existence of asymmetric dynamic global solutions to Einstein's equations in general relativity. Participants highlight that while significant progress has been made over the past 104 years, most existence theorems are confined to small perturbations of highly symmetric solutions. Notably, the global existence theorem established by Choquet-Bruhat and Geroch in 1969 indicates that maximal hyperbolic Cauchy developments exist, yet understanding of these solutions remains limited. The conversation emphasizes the need for research that addresses more realistic physical configurations beyond traditional models like the FLRW solution.

PREREQUISITES
  • Understanding of Einstein's equations in general relativity
  • Familiarity with global existence theorems in mathematical physics
  • Knowledge of the FLRW solution and its implications in cosmology
  • Awareness of perturbation theory in the context of differential equations
NEXT STEPS
  • Research the implications of Choquet-Bruhat and Geroch's 1969 global existence theorem
  • Explore advanced topics in asymmetric dynamic solutions in general relativity
  • Investigate recent studies on realistic physical configurations in cosmology
  • Learn about perturbation methods in the context of Einstein's equations
USEFUL FOR

Physicists, mathematicians, and researchers focused on general relativity, particularly those interested in the development of global solutions and their applications in cosmology.

Heikki Tuuri
Messages
164
Reaction score
64
https://link.springer.com/article/10.12942/lrr-2005-6

https://en.wikipedia.org/wiki/Exact_solutions_in_general_relativity

http://www.numdam.org/article/SEDP_1989-1990____A15_0.pdf

A moderator removed this off-topic discussion from another thread. Does anyone on the Physics Forums have expertise on the existence of global solutions of general relativity?

As you see, people have worked very hard for 104 years to prove existence theorems. As far as I know, they are all limited to small perturbations of highly symmetric solutions.

Can anyone point to research that might have progressed closer to realistic physical configurations?
 
Physics news on Phys.org
Heikki Tuuri said:
Can anyone point to research that might have progressed closer to realistic physical configurations?
Part of the problem (the main problem) was your personal and overly restrictive view of what constituted a realistic physical configuration. For example, you objected to the FLRW solution as being unrealistic whereas most scientists and particularly cosmologists consider it realistic.
 
Heikki Tuuri said:
As you see, people have worked very hard for 104 years to prove existence theorems. As far as I know, they are all limited to small perturbations of highly symmetric solutions.
That is not true. Global existence (as in the maximal hyperbolic Cauchy development) is a result from 1969 (Choquet-Bruhat, Geroch). What is limited is the understanding of those solutions.
Can anyone point to research that might have progressed closer to realistic physical configurations?
What do you mean by realistic physical configuration?
 
Heikki Tuuri said:
A moderator removed this off-topic discussion from another thread.

Which is completely irrelevant to this thread. Please do not carry over whatever issue you might have with the moderators in a previous thread to new threads.
 

Similar threads

  • · Replies 124 ·
5
Replies
124
Views
17K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 11 ·
Replies
11
Views
4K
  • Sticky
  • · Replies 2 ·
Replies
2
Views
503K
Replies
24
Views
8K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 5 ·
Replies
5
Views
5K