Hi Sascha - best for 2013 and yes it has been a long time and no won't bring up incompressible fluids. Still there is something about p as source term(s) in T (stress-energy tensor) that imo just doesn't look at all Kosher. Up to you whether to here this out but will present it anyhow. Moving right away from exotic dark energy, suppose we consider a mundane example involving just the usual elastic stresses in a solid. A straight and uniform elastic rod set into fundamental axial mode vibration - sinusoidal stretching and compressing along rod symmetry axis. I think we agree this constitutes primarily a linear mass-quadrupole oscillator (superposed on the rod static mass term). So according to GR we expect to have an exceedingly weak but finite source of quadrupolar GW's (gravitational waves) - plus much weaker higher moment contributions - but with exactly zero contribution from lower order moments (monopole and dipole terms).

Given a fundamental frequency of rod free oscillation f, and assuming negligible damping, then the standard GR formula predicts an overwhelmingly dominant contribution to GW output will be at frequency f and owing to the rod time-changing mass quadrupole moment of amplitude Q ~ MR^2 ( M the rod mass, R the axial excursion amplitude) e.g. aether.lbl.gov/www/classes/p139/homework/hw12.pdf (sec't 3.1). This stems from the momentum flow-rate term T0i (or Ti0) in T, or rather it's time derivatives.

A very much smaller addition can be expected at a frequency 2f owing to the quadratic (in velocity, stress) contributions to T00 (time-time energy term) from Kinetic energy of axial motion and elastic energy of axial compression/tension, respectively. Although these terms add at all times to give a constant total energy, they are in phase quadrature and moreover their distributions are not spatially coincident - cosinusoidal vs sinusoidal wrt axial location along the rod. Given that at any given instant both the KE & PE densities are of the same sign all along the rod, this implies a dominant monopole, not quadrupole contribution from each! (Yes I know standard GR position says such terms cannot be present or must always cancel - but where and how?)

What of the notional contribution from axial rod stress 'all by itself'? Well firstly, unlike the stress contribution to elastic energy which is generally a quadratic function of stress, 'pure' stress term Tii evidently fluctuates at frequency f, not 2f. Hence if there is any GW output from fluctuating Tii, it will be at frequency f. Just as for the dominant T0i contribution. So what, you may be thinking - all this must have been well understood from near the dawn of GR. Maybe not really. Thing is, if one inspects the spatial distribution of the axial Tii term, what do we see? The rod fluctuates between essentially half-sinusoidal tensile and compressive stress distributions - with maxima clearly at the rod centre and zero at rod ends.

Again, so what you are thinking. Well although a spatial half-sinusoidal distribution constitutes a multipole moment, it must be clear that, just as for the above KE & PE terms, by far the dominant Tii contributed term re GW generation will be a monopole moment - *necessarily so since the stress distribution at any given instant is all of the one sign*. In the case of uniform pressure (uniform triaxial stress) it is customary to simply sum for each component scalar-like. Implying that uniaxial stress acts like a scalar contribution also. Do I need to spell out what that implies? It spells out *GW monopole radiation* - owing to the Tii 'pure stress' term alone!

Quite apart from the f vs 2f frequency difference owing to Tii and T00 source terms above discussed, other factors preclude cancellation of the T0i monopole moment contribution term by any of the others (KE/PE T00 terms in particular). For example, make the rod N times stiffer: Young's modulus E -> NE (but same mass density), and we easily find that if peak stress amplitudes are held constant, all the other multipole amplitudes owing to terms - T0i and T00's, tend to zero as N, and thus E, tends high. Necessarily so since the vibrational amplitude declines as 1/E. Thus fundamental mass quadrupole moment Q, and KE/PE amplitudes, will decline (frequency f rises as sqrt(N), but that applies to all terms). Of course monopole and quadrupole terms will have very different frequency dependence (f^2 vs f^6 respectively) - but this is only an issue if one has already conceded the existence of non-zero monopole terms! Anyway this all highlights the strangeness of the Tii term as GW source - 'magically' there is no direct relation to E, as stress and stress alone counts, quite divorced from energy density. Such is the purported character of stress 'all by itself'. When I last checked, three differing monotonic functions can meet (or cancel) at one point at most. Go figure.

If this has been followed without going crossed-eyed, the obvious objection (thrown at me in a prominent physics forum site) seems to be, as afore mentioned, that it can't be true. Since in GR the stress-energy tensor is automatically a conserved quantity and together with conservation of momentum, this 'guarantees' only quadrupolar and higher moments can survive re GW generation. Well as a layman I am certainly no GR expert but if the latter is true then there sure appears to be a clear philosophical/logical conflict here given that in the obviously weak (ultra-weak really) gravity regime pertaining to a rod oscillator, it surely is legitimate to cleanly separate out the various T contributions. Contributions with e.g. markedly different functional dependence on material parameters, and generating markedly different multipole moments.

In summary, best I can tell example of an axially vibrating rod confronts one with a dichotomy. Looked at in terms of individual T contributions, there are 'forbidden' low-order GW multipole terms, including monopole terms at two differing frequencies. This is forbidden in GR and so I am told cannot be an issue when the standard GR method of solving such a scenario is adopted. Maybe so according to standard GR, but imo this implies stress-energy contributions must be made to do some truly bizarre gymnastics, even in the limit of very weak gravity/energy regime. Seems more likely one needs to take a harder look at whether 'pure' stress terms really do contribute as gravitational source and hence whether stress should be excised from the stress-energy tensor. Is there actually any hard observational evidence pure stress/pressure does contribute as per T implies?

This still leaves the matter of apparent monopole contributions from the undoubtedly real T00 elastic energy and KE contributions, but I consider that secondary to the role of stress here.
OK so the stats suggest I'm utterly wrong-headed and this little piece has justly earned a crackpot label, but then again an intelligent critique following a thoughtful read would be appreciated. Either way, not something to stress over :)