doubt about gravitational waves

TrickyDicky

The usual derivation of the wave form equations from the GR field equations is done in the weak field, linearized approximation of the GR theory. In this limit, that ignores non-linear contributions and that gives accurate results when used to predict solutions for problems in the Newtonian limit (classical tests of relativity, more recently rates of orbital decay of binary system pulsar-see Hulse-Taylor pulsar..) the background space is the static flat Minkowski spacetime.

So this linearised EFE when used in the theory of gravitational radiation are mixing a static spacetime that by the Birkhoff's theorem doesn't allow gravitational radiation to exist(this is related to the specific features of static spacetimes that I won't go into in this post) and the interpretation that the equations similarity to wave equations and more specifically to the tranverse EM waves of Maxwell theory (see GEM equations, etc) must mean the existence of gravitational type of waves.

I see here, that at least theoretically, something doesn't fit completely, but maybe it's just my impression, I just would like to understand gravitational waves within the conceptual framework of GR. For instance, if the linearized EFE look like EM wave equations why not consider them EM radiation to begin with?
Moreover, if the background spacetime where the linearized equations are similar to wave equations forbids gravitational type of waves, is this not a sign that maybe they are not gravitational waves, but plain EM waves radiated from the mass quadrupole (which would justify the observed orbital decay in binary systems like the Hulse-Taylor pulsar?

Of course, I'm not proposing any alternative, just would like to know how is this addressed from the point of view of mainstream GR theory, or how any of my perhaps naive premises are not correctly applied to this subject (wich surely are not).

Mentz114

I found the derivation of GWs from the linearized theory somewhat unconviving, but there are exact (vacuum) solutions of the field equations that look like plane-fronted waves with parallel rays (pp-waves). These solutions have Riemann curvature associated with the waves.

What I've never seen is a solution for, say, an oscillating mass that radiates gravitationally. I'm not sure if such a solution can exist because the EMT of the source would not be conservative, whereas the Einstein tensor is guaranteed to satisfy G^mn_;n = 0.

Bill_K

No, gravitational waves are very well understood by now, both theoretically and computationally. Including nonlinear effects, and coupling to a time-varying source. The linearized solutions look like electromagnetic waves only in the sense that they obey the wave equation. Apparently the derivations you've read are oversimplified.

Bill_K

Exact solutions tend to be unrealistic. The solution to the type of situation you describe will need to be done numerically. Several groups have now computed the collision of two black holes, including the gravitational radiation that is emitted. See http://www.nasa.gov/vision/universe/...ies/gwave.html.

TrickyDicky

Interesting, do you have any reference on those solutions?

Bill_K

Wikipedia has an article on them. As it says there, they were first written down by Hans Brinkmann in 1925.

George Jones

Chapters 17 - 21 of Exact Space-Times in Einstein's General Relativity by Griffiths and Podolsky,

http://www.amazon.com/Space-Times-Ei...2781883&sr=8-1.

TrickyDicky

This doesn't even try to answer in the context of what I posted.
What would you say about the background static spacetime being incompatible with gravitational radiation?

Well. I'd say the fact that they should propagate precisely at c, is another point to consider when referring to the similarity. But certainly they need not be EM waves. Still, since GW are so well understood by now, would you explain to me what exactly is oscillating in gravitational waves? curvature?

TrickyDicky

Thanks, still as Bill K has just pointed out exact solutions tend to be unrealistic, and I would add that those solutions referred to in the Podolsky book are not very realistic.
What this tells us is that being an exact solution of the EFE doesn't guarantee anything, as there are many unphysical solutions that have nothing to do with our universe.

George Jones

Helicity. The polarization states of gravitational and electromagnetic radiation transform differently under rotations.

Nabeshin

I'd like to emphasize this. There's really no doubt that Einstein's GR does contain gravitational waves. When we actually code in his equations and evolve the binary black hole spacetime, we get very clearly GW coming out. This is something I look at on a daily basis, so I'm quite confident in it

Bill_K

You mentioned Birkhoff's Theorem, but that applies only to spherically symmetric perturbations. Gravitational waves are quadrupole and higher.
Gravitational radiation is characterized by a 1/r term in the Riemann curvature tensor. Large amplitude waves need to be treated numerically, but for example you can talk about small amplitude perturbations of the Schwarzschild solution. In second order one sees that the Schwarzschild mass decreases with time, corresponding to the energy being carried away by the waves.

Mentz114

I've been reading back copies of 'Matters of Gravity' and there's a fairly detailed description of the numerical methods in this spring 2006 issue.

http://www.phys.lsu.edu/mog/pdf/mog27.pdf

Extract:

TrickyDicky

That's what I'm saying, that there seems to be some incompatibility between a background spacetime that is spherically symmetric and the fact that this kind of spaces don't admit GW kind of perturbations. But rephrasing it doesn't help me understand it.

Again, how can the Schwarzschild spacetime, wich is also spherically symmetric and static say anything about GW? It's so confusing.

TrickyDicky

I know GW are postulated to have different helicity than EM waves, in fact the boson proposed for the grav. radiation, the graviton (that BTW hasn't been detected) has spin 2 in contrast with the spin 1 of the EM radiation boson (the photon) so it is straightforward that they should have different helicity.
The issue here would be how does that postulated difference translate to observational tests, and there one faces the problem that gravitational waves (or gravitons for that matter) have not been directly detected so far, and according to some people they might not be detected in many years if ever, so this raises problems with falsability, since the indirect observations that makes us suspect the existence of GW (orbital decay of certain binary sistems) can't distinguish helicity differences.

Mentz114

Do the perturbations, in this case, destroy the spherical symmetry ? Like a short-lived dimple ?

TrickyDicky

Thanks, at least someone else acknowledges that all is not so nice and easy with the BH binaries numerical simulations as Bill k and Nabeshin seem to imply