Indeed it does. Think about binary pulsars. They can be well approximated as two point masses following their Einsteinian orbits; so both point masses follow geodesic trajectories. Yet as a result of the energy loss due to gravitational radiation, they slowly inspiral. The change in their orbital period is one of the indirect ways that we have been able to detect the existence of gravitational radiation to date.

@ Toth: Yes indeed, I agree with you but I could only see incomplete works, in them the computation is (on one hand) focused on the presence of a "perturbation to the metric" that propagates, and this is exactly the gravitational wave, on the other hand the loss of energy of a system computed through a series of approximations [PNE i.e.]. What I have never been able to read (and wonder if I can find it somewhere) is the mechanism that causes the system (composed by source-masses... using wrong words but getting the idea) "generating" the gravitational radiation.... more or less: if In "classical theories of gravitation" the gravity-wave is for the in a gravitational field; the information of a change in the distribution of energy and momentum of matter results in subsequent alteration, at a distance, of the gravitational field which it produces, [in a more physically correct sense] how can you have "such a change" if the Einstein equations are fully self-consistent: each element (mass-energy-momentum) source will follow exactly its geodesic...? the electromagnetic analogy says that a charge emits only if accelerated. If it goes with a uniform rectilinear motion (which in a Euclidean space-time is equivalent to the geodesic) does not emit.

@ Toth: U say

"two point masses following their Einsteinian orbits;..[cut].... they slowly inspiral"

and this is a measured result.

I am asking if the "closed form" solution for Einstein Equation SystemSet describes the same behaviour, i.e. a spiraling orbit for both masses [for the calculations Im referring to Weinberg (gravitation) chapters 9 , 10 & 2 and 4, just the pointlike massive particles]

A "closed form" solution is probably too much to ask, since only very special cases (e.g., Schwarzschild) in general relativity yield closed-form solutions. However, other cases can be investigated using either numerical methods or some form of valid approximation scheme.

Weinberg's book is very good but it predates the discovery of binary pulsars with a detectable change in orbital frequency due to gravitational radiation. This topic, however, is discussed in sec. 4.4 of Wald's General Relativity. The bottom line is that the theoretical prediction is in excellent agreement with the actual observation, and the prediction is treating the source as two point masses following geodesic orbits.

The answers above are very good. In fact any object with mass (which is just about everything) will give out gravitational waves. These will in most cases be miniscule and basically undetectable but it will result in the object loses a very very small amount of mass. This process is virtually 100% efficient. Only extreme conditions where neutron stars or black holes combine will detectable waves be given out in the form of pulses. I believe these will be detected in the next few years with the new round of gravitational wave detectors coming on line.

Graeme Melville: not exactly [any object with mass  will give out gravitational waves] -- if we are neglecting quantum effects (like Bekenstein-Hawking radiation).

Say, isolated body at rest will produce no radiation (again, if we are talking about classical GR), nor will some other symmetric systems (like radially pulasating spherically-symmetric one, or axially symmetric uniformly rotating one).

Usual source of GW is the third time derivative of the quadrupole moment the system stress–energy tensor; it must be nonzero for producing GW. Or, more exotic, the l-th time derivative of the l-th multipole moment. 

Dear V. Fulcoli,  your question is very good!  It is important conceptual question and it does not depend on the reality of gravitational radiation (so the Toth’s anser is incorrect).

I agree with you that the geodesic motion in GR is the analogy of the rectilinear motion in Euclidian space just as the consequence of the Equivalence Principle, according to which free fall is equivalent to an inertial  motion.

It was already had been discussed in the professional literature that there is a conceptual paradox of the electromagnetic radiation from free falling charge. The question is about equivalence between a charge in free fall and a charge in rest at the lab table in the homogeneous gravity field. The free falling charge is accelerated and must radiate energy according to classical formula  dE/dt=(2/3)e2g2/c3 (ergs/sec). However the free fall is equivalent to inertial motion and this charge must not radiate. Another form of the paradox is that the charge at rest in gravity field will radiate energy because such reference frame is equivalent to accelerated frame.

The same is valid also for gravitational radiation.

The root of the paradox lays in the equivalence of inertial motion with accelerated motions in GR. This also related to the well-known conceptual problem in GR with definition of the energy-momentum of the gravitational field.

Let us try to look at this question using B. Mashhoon's concept of acceleration length (cf. Phys. Lett. A vol 143, nb 4,5,  pgs 176-182). The acceleration length "l" associated to a body being accelerated by a gravitational field is inversely proportional to its tidal acceleration: l=c2/a

A mass falling freely in a CONSTANT (homogeneous, uniform, isotropic) gravitational field cannot radiate energy under the form of gravitational waves for the same reason that an electric charge falling freely in a homogeneous gravitational field cannot radiate electromagnetic energy. In both cases locally the mass and the charge behave like inertial bodies. This is coherent with the definition above of acceleration length, since in the present case the acceleration length is infinite (null tidal acceleration). Indeed inertial observers have infinite acceleration length. A similar rational can be made if the accelerations are from non-gravitational origin (constant acceleration vectors do not lead to radiative effects cf. discussion thread on "Does a uniform accelerated charge radiate?").

For the case of a gravitating system like for example the binary Hulse-Taylor Pulsar (PSR 1913+16) although the bodies follow geodesics, the tidal accelerations supported by the binary are not null anymore, leading to a finite acceleration length "l", and to the possibility of Gravitational Waves (GW) emission by the binary system. Thus dissipating energy and contributing to the decay of the orbital motion of PSR 1913+16. The acceleration length "l" limits the applicability of the concept of locality to the binary pulsar. The more the Gravitational Waves wavelength L approaches the acceleration length the less on can apply the hypothesis of locality to the binary system. Back reaction radiation terms appear in the pulsar equations of motion, and cannot be removed on the basis of the principle of equivalence. In the limit that L~l It is impossible to regard the Gravitationally radiating pulsar as momentarily inertial.

Can't the gravitational ‘radiation’ described by GR simply an oscillating gravitational field signal received by an observer rather than any quantum particle/wave emission that might be described by particle physics?

I understood the oscillating signal produced by Quasars, etc., to be simply the rapid juxtaposition of two gravitational fields representing an oscillation of disparate spacetime ‘curvatures’ presented to a distant observer. This view seems to explain why some oscillating systems are not thought to produce gravitational waves. See http://en.wikipedia.org/wiki/Gravitational_wave#Sources_of_gravitational_waves.

@James Dwyer:

Hi

U wrote: "Can't the gravitational ‘radiation’ described by GR simply an oscillating gravitational field signal received by an observer rather than any quantum particle/wave emission that might be described by particle physics?"

Yes. I agree with Whitham wave definition: A wave is the mechanism by which information is transferred from one place to another in the universe. And that's exactly the point:

Let us analyze a scenario exclusively gravitational (I say this to put emphasis on the fact that here they are excluded computations related to, for example, stars treated as large self-gravitating structures sustained by several interactions, not only gravity but also of other type ... for example electromagnetic, weak strong and relatively to the Pauli exclusion principle as the Fermi liquid: only a gravitation action). In this scenario, when you're away, you as a test-particle let's say a massive probe distant from a pair of gravitating point-like masses, do you need to be informed about such an orbital motion? This is the point.

I imagine because (in the Einestein Equation set) the writing of the source term in those equations, for a Tmn consisting of 2 point masses, is doing by the sum of 2 deltas-dirac integrated on their (of the 2 massive-particles) world-lines and whith the g factor, then this means that it is an implicit knowledge of the structure of the whole spacetime-manifold that them are automatically generating.

But following a PNE calculation it seems to appear an evidence for a Energy loss of the system: why? Is it correct? In the literature there is a bit of confusion: someone says that this energy loss is simply related to the 4pole moment of the macroscopic gravitating bodies (stars), someone says that this is instead an effect of the reciprocal-orbits. I can only point out a plausible convergence of the series, but I have no certainty due to the absence of an exact solution.

The gravitational wave has a meaning: in a "empty" space  u could see a moving disturbance... and treating the small fluctuation u can write it as a Dalambertian with a known solution for retarded waves with a 1/|r-r'| factor... a wave!

This is exactly what Feynman's Field Gravity approach tells bout gravitational waves.

Hence there is no such paradox in the treating gravitational interaction as the symmetric tensor field in Minkowski space.

If the contraction/expansion of dimensional spacetime corresponds to any physical component of vacuum energy, its repeated reconfiguration by a rotating gravitational system must reduce that system’s energy. The question then is whether any particles of matter are emitted in the process. As I understand the concept of virtual particles, considering them to be physical entities (not necessarily complying with the mass, etc., of standard model particles) is a computational convenience. More likely field energies are affected by more direct exchanges – unless we are required to forcibly fit such exchanges into the restricted 'framework' of existing quantum theory…

@Yurij V. Baryshev:

Hi... I agree wU

the question arises because I'd like to investigate the question a littlebit wider. I'll try to explain. We know that a great desire of physics is given by the attempt to unify all interactions, either from the point of view of geometrodynamics (and I think to KaluzaKlein) or from the point of view of field theory.

"To Unify" is a concept that tends to place as a unique entity that was before identified as a many-multi interactive-action... but compared to what?

When we attempt to unify ... what do we want to reach? Unifying forces or "consolidate" the information?

so  my question then arises spontaneously when I think about the differences between electromagnetism and gravity.

If it really there was a superstructure electro-gravitational, when should it occur? looking at the deep distinction between the two phenomena....

@James Dwyer:

I know that a "exchange boson gauge" relies on the of the Action ... i.e. a little change in the 4d (or more) path of integration makes a virtual (or not) particle... but here we are set at a different semantic level ... more or less the same thing that happen when u read at the 2nd quant process for the elect-magnetic field: u use the de Broglie approach also for the Maxwell equation, applying the 1/ih factor to Poisson brackets as commutators for Observable operators... but the role of the Schroedinger PSI function in this case is carried out by whom?

V. Fulcoli,

Sorry I neglected to formally introduce myself as a retired information systems analyst, so that my comments could be considered in the context of my capabilities. I certainly never want to misrepresent my qualifications.  Please see my profile.

However, as I understand your challenging response, in answer to your question - “… the role of the Schroedinger PSI function in this case is carried out by whom?" – I can only reply euphemistically, ‘Someone outside the ‘framework’ of existing quantum theory’.

I found these two very interesting papers from which to extract a lot of information

(by Volodya Belinski )

http://arxiv.org/pdf/1211.3964v1.pdf

http://arxiv.org/pdf/0706.1981v1.pdf

There is nothing interesting in these references, they are not about our discussion of the concept of gravitational wave in GR.

@Yurij: I said about "extract information" and not "capture information"... its hard to find what you want if you expect to find it in the way you want it :)

Have you extracted information from recent paper by Hawking  ( see  http://www.nature.com/news/stephen-hawking-there-are-no-black-holes-1.14583 ) about non-existence of Black Holes in correct gravity theory?

According to this new point of view of the primary author of Black Holes now all papers about classical (non-quantum) structure of  "Black Holes" have no interesting information.