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Results tagged with general-relativity
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user 5993
For questions about mathematical problems arising from general relativity, the branch of physics which provides and studies the currently accepted geometric description of gravity.
4
votes
Accepted
Conditions for existence of Penrose diagrams
There is no definitive answer to your specific question, so I'm going to talk around the topic and hope that it's informative.
As you've noted the classical examples all basically look like special c …
- 490
1
vote
Conjugate point to spacelike hypersurface
There are two cases: Jacobi fields defined in terms of a geodesic spray from a point and a geodesic spray from a surface. In both cases the differential equation that defines the Jacobi tensor is the …
- 490
7
votes
Penrose’s singularity theorem
Wille's answer is technically true, but he doesn't talk about the historical context of the result. I think that is important for understanding why such a "simple" result is deserving of a Nobel prize …
- 490
2
votes
Eikonal equation and double null coordinates
Per Willie's answer, locally this is the same thing. The global situation is, predictably, very different. I don't know anything specifically about the eikonal equation, but I do know about global sol …
- 490
8
votes
Einstein field equations in perspectives from PDE and functional analysis
For a through overview of the use of functional analysis in General Relativity read Alan Rendall's "Partial Differential Equations in General Relativity". It's basically an elongated literature review …
- 490
3
votes
Principal bundle approach to general relativity
You might enjoy Bleeker's book "Gauge Theory and Variational Principles" (http://www.amazon.com/Gauge-Theory-Variational-Principles-Physics/dp/0486445461). His focus is definitely more on particle the …
- 490
1
vote
Usage/Application of Raychaudhuri equation in Riemann geometry or pure maths
The Raychaudhuri Equation is called the Raychaudhuri Equation because of a physist called Raychaudhuri. In mathematics the same equation occurs, for the reason you have pointed out, but it is called s …
- 490
1
vote
Lower bound for domain of exponential map on Lorentzian manifolds
You've waited a long time for an answer. And I am surprised that no one has written one.
Let $M=\mathbb{R}\times(0,\infty)$. The exponential map isn't defined at $(x,t)$ for vectors $(u,s)$ with $s<-t …
- 490