Hello,

I`ve read Marcus thread on General relativity and I have a few questions concernig the problem as I do not understand GR at all I am merely interested in subject. I am creating new thread as I didn`t want to flood that excellent thread by my stupid questions .

1) Some physicists today search for gravitational waves. I suppose these are some cases of vacuum solution to EFE same as EM waves are solution to Maxwell equations? If so they would be something like propagating "wave" in metric that would through connection look like propagating wave in curvature? What these waves represent? (change in distribution of matter??? or?) When they should be created and why we didn`t detected them yet? Would they transport energy same as EM waves and if so wouldn`t it mean that they have to have momentum -> act as force?

2) Marcus said that from infinite possible connections Einstein chose Levi-Civita connection as it has zero stress. What would mean that property of spacetime is stress? Can it be somehow experimentaly verified that our spacetime is stress-free? Or is it possible that some other connection would get better results than Levi-Civita? Or does all connections yield same results and they are just some kind of gauge?

3) Cosmological constant. From our observation of red shift shouldn`t we be able to quantify it? Does additional term changes solutions to EFE a lot or does it just add some kind of time dependence or ???

4) The source term of EFE is Energy-momentum tensor. But shouldn`t GR TEM tensor contain energy tensors of all forces basically? Same as for example EM field of electron contribues to it`s inertia. Could deviation from real solution be relevant if one ignores for example EM stress tensor? How about other forces? Is gravity TEM tensor dominant source?

5) Somewhen someone said that you can formulate GR from Lagrangian. Basicaly get EFEs as Euler-Lagrange equations. What I don`t understand is that Lagrangian is defined as scalar in spacetime (basicaly). How can one make connection between Lagrangian and curvature/metric? Also if such Lagrangian exist shouldn`t it among other symmetries be gauge invariant? Shouldn`t then be there gauge field accompanying?

6) As EFEs contain only Ricci tensor how is it possible that we doesn`t lose some information about Riemann tensor? Or does Ricci tensor somehow contain all necessary information about curvature? Also are EFE`s solutions unique?

Thanks in advance for your time