Monopole Gravitational waves exist?

Question

GR says that monopole gravitational radiation does not exist. I understand the reasons for this.

However there is this effect (which seems to me to have the hallmarks of a wave). Paper at arXiv:

Monopole gravitational waves from relativistic fireballs driving gamma-ray bursts (http://arxiv.org/abs/astro-ph/0309448)

I would like some feedback on that paper, my thoughts on it are below, which may or may not be relevant.

Basically what happens is that you have a mass that sheds energy. So if you are standing at a point outside the mass, the gravitational potential changes very quickly as the ejected mass passes by you. Since we detect the gravitational field as the slope of the potential, it seems there will be a boost applied to our motion as the potential changes.

This change in motion is why I think that the paper has the correct name - these are waves.

The author of the paper had no trouble calling this effect a monopole gravitational wave, but is it properly called a gravitational wave?

Answer 1

These kind of effects apply to any kind of mass or energy. A massive particle moving at below the speed of light will carry a "subluminal gravitational wave". Dipolar radiation will carry a "dipolar gravitational wave" etc.

In principle, you can assign the label "gravitational wave" to any kind of gravitational field propagating along with some matter-energy object. But this is not usually done. A more purist viewpoint would be to call the free gravitational waves as the only gravitational waves. I.e., if it is a vacuum excitation of the space-time itself, it is a gravitational wave, if it is actually the gravity associated with some object, it is not. Such gravitational waves radiated from isolated sources can indeed be only quadrupole.

However, this line is harder to draw in the case of null (moving at speed of light) matter. In that case, you often do not know which part is the "free" wave and the one "carried along" because they would both move at the speed of light along the matter/radiation. And this is also a fundamental issue; there is no truly fundamental difference between the "space-time at rest" and the "vibrating space-time" through which the wave is passing. We are able to speak of the difference between a "wave" and a "non-wave" only thanks to a predefined meaning of a "still background". But when you are for example in the thin shell of gamma radiation travelling away from a source, the "correct background" is basically impossible to define.

Hence, people often talk about waves dragged with null matter simply as gravitational waves and do not make a distinction between the "free" and "dragged along" part (Griffiths & Podolský have a few chapters with examples). In the paper you link, the distinction could be made because one could show that there is no extra freedom in the polarization or strength of the wave. Simply put, the gravitational wave has no free properties and it is fully determined by the shell of gamma radiation (up to non-physical gauge transformations). So we could either call the mentioned excitation in the metric a "monopole wave" or a "dragged-along gravitational field", it is really just a question of a finer naming convention.

Answer 2

I think it is important to emphasize that monopole gravitational radiation does not exist in a vacuum.

In the gamma ray fireball case, we experience something like a monopole gravitational wave because a chunk of the progenitor's mass energy is expelled in the form of (in the idealized case) a spherically expanding shell of radiation. While we are outside this shell of radiation, we see no change in the gravitational field, but as the shell of radiation passes by us, we see a corresponding reduction in the gravitational potential. Depending on how thin the shell is (how instantaneous the burst was) this reduction in potential can be accompanied by a sharp gradient.

Having said that, I would be reluctant to call it a gravitational wave. Unlike "true" gravitational waves, this "wave" does not exist on its own. Rather, it effectively "surfs" on the expanding shell of radiation. If somehow the radiation was stopped (e.g., if we surrounded the fireball by a concentric, spherically symmetric perfect mirror) this gravitational "wave" would be stopped, too. No real gravitational wave can be shielded this way.

I should also mention that this effect is by no means confined to relativistic fireballs. In principle, the same monopole "wave" can be experienced in any expanding or contracting spherically symmetric object, so long as the observer is inside the object.

So personally, I would refrain from calling it a gravitational wave. However, I can see why, from an observational perspective, it may be tempting to call it that nonetheless. As the radiation wavefront from a fireball passes us by, the monopole gravitational "wave" would be present, too, and may in principle be observed. However, given the typical distances to such fireballs, their unpredictability, and the timescales of the explosion, I suspect that the effect would be much harder to detect than quadrupole radiation from inspiraling binaries.