Is general relativity holonomic?

[Ganesh Ujwal]

Is it meaningful to ask whether general relativity is holonomic or nonholonomic, and if so, which is it? If not, then does the question become meaningful if, rather than the full dynamics of the spacetime itself, we consider only the dynamics of test particles in a fixed globally hyperbolic spacetime?

For the full problem, my immediate conceptual obstacle is that it's not obvious what the phase space is. In ordinary mechanics, we think of the phase space as a graph-paper grid superimposed on a fixed, Galilean space.

The definitions of holonomic and nonholonomic systems that I've seen seem to assume that time has some special role and is absolute. This isn't the case in GR.

There is a Hamiltonian formulation of GR, which would seem to suggest that it's holonomic.

In classical GR, information can be hidden behind a horizon, but not lost. This suggests that some form of Liouville's theorem might be valid.

The motivation for the question is that Liouville's theorem is sort of the classical analog of unitarity, and before worrying about whether quantum gravity is unitary, it might make sense to understand whether the corresponding classical property holds for GR.

[Mordred]

Not really sure on this. I've seen both solutions on the Eistein field equations.

 

http://www.google.ca/url?sa=t&source=web&cd=11&ved=0CBoQFjAAOAo&url=http%3A%2F%2Farxiv.org%2Fpdf%2Fgr-qc%2F9502020&rct=j&q=is%20the%20Einstein%20field%20equations%20holonomic&ei=TF6fVK72JYSGyQS6joFQ&usg=AFQjCNHy-kpcgybVtV9dV2g8RHZMMjVGVg&sig2=YqL7xP_teDJxgDRiyeoDTg&bvm=bv.82001339,d.aWw

http://www.google.ca/url?sa=t&source=web&cd=14&ved=0CC0QFjADOAo&url=http%3A%2F%2Fwww.emis.de%2Fjournals%2FUIAM%2FPDF%2F41-267-272.pdf&rct=j&q=is%20the%20Einstein%20field%20equations%20holonomic&ei=TF6fVK72JYSGyQS6joFQ&usg=AFQjCNGpWG66xeRtknG9WevXVfUFVkqvpw&sig2=7JvkPpJGymHWoDT_HIpxdA

The above apply holonomic solutions

 

Here is some examples of nonholonomic

 

 

http://arxiv.org/abs/1010.0647

http://arxiv.org/abs/0704.3986

 

Your guess is as good as mine

Lol if not better than mine

Edited December 28, 2014 by Mordred