Gravitational Waves: Questions on Mass & Escape Velocity

[.Scott]

A few years go, we detected a gravity chirp from the collapse of binary black holes.
The initial total mass was about 21.7 solar masses. The end result was about 20.8 solar masses.
The difference was presumably contained in the gravity wave.

I believe, under the right conditions, an object orbitting this event could suddenly find itself traveling faster than escape velocity once the gravity wave passed it.

Now let's consider a machine that is 21.7 solar masses that can emit two laser beams, one each from its North and South pole. And in an instant (or within a 300msec chirp), can lase off 0.9 solar masses.

This time our orbiter will be in orbit around the equator. And as before, it will soon find itself out of orbit.

So my questions are:
Would the "wave" that passes the orbiter in the second case also be a gravity gravitational wave?
Would it be a mass-carrying gravity gravitational wave?
Is there something inherent in accelerating mass - as was done with the lasing - that will also create a gravity gravitational wave with mass?
Since gravity gravitational waves pretty much pass through everything, what is the "ending state" of these mass-carrying waves? Mustn't we have gravity gravitational waves originating from the Big Bang criss-crossing our galaxy?

 

[PeterDonis]

The difference was presumably contained in the gravity wave.

Gravitational wave, not gravity wave. The term "gravity wave" refers to something very different:

https://en.wikipedia.org/wiki/Gravity_wave

 

[PeterDonis]

Would the "wave" that passes the orbiter in the second case also be a gravity wave?

I think there would be a gravitational wave emitted, yes, though it would be quite different in nature from one emitted by a black hole merger.

Would it be a mass-carrying gravity wave?

The term "mass-carrying" is not a good one. Gravitational waves are waves of spacetime curvature: they have zero stress-energy. So they don't have any "mass".

Note that, in your second scenario, most of the difference in mass between the initial object and the final object would be contained in the laser pulses that were emitted. But laser pulses don't have any "mass" either: they carry energy (so do gravitational waves) and they have stress-energy (as gravitational waves do not), but their stress-energy is traceless (because they're source-free EM fields), so they have no "mass" (for the same reason that photons are massless) and travel at the speed of light.

The best way of describing what I think you are trying to describe here is that gravitational waves carry energy, and can transfer at least some of the energy they carry into objects they pass through. However, their ability to transfer energy is much weaker than that of EM waves. See below.

Mustn't we have gravity waves originating from the Big Bang criss-crossing our galaxy?

That is what most physicists believe, yes. As I noted above, gravitational waves carry energy and can transfer some of their energy into objects they pass through, but their ability to do so is very weak. So they basically just keep traveling on forever, weakening slightly as they pass through objects.

 

[.Scott]

How do gravitational waves interact with black holes? I would imagine that whatever energy is being carried by the section that reaches the event horizon of the black hole would be fully absorbed by the BH - adding to its mass. This would leave a gravitational wave shadow just beyond the BH. With gravitational waves criss-crossing the area of a BH from all directions, all leaving shadows, would this make the BH appear to have more gravitational attraction than would be expected?

 

[PeterDonis]

I would imagine that whatever energy is being carried by the section that reaches the event horizon of the black hole would be fully absorbed by the BH - adding to its mass.

If the wavelength of the gravitational wave were small enough to fit inside the hole, I would agree. I'm not sure about a gravitational wave with a wavelength much larger than the hole's size (which is basically the hole's mass in geometric units). I think such a wave might be perturbed by the hole and give up some of its energy to it, but not all.

would this make the BH appear to have more gravitational attraction than would be expected?

No, because, as you say, the hole's mass would be increased by any energy it absorbed from gravitational waves, and to an observer far away on the other side of the hole, it doesn't matter what contains the energy, its gravitational effect is the same either way.

 

[pervect]

A few years go, we detected a gravity chirp from the collapse of binary black holes.
The initial total mass was about 21.7 solar masses. The end result was about 20.8 solar masses.
The difference was presumably contained in the gravity wave.

I believe, under the right conditions, an object orbitting this event could suddenly find itself traveling faster than escape velocity once the gravity wave passed it.

Now let's consider a machine that is 21.7 solar masses that can emit two laser beams, one each from its North and South pole. And in an instant (or within a 300msec chirp), can lase off 0.9 solar masses.

This time our orbiter will be in orbit around the equator. And as before, it will soon find itself out of orbit.

So my questions are:
Would the "wave" that passes the orbiter in the second case also be a gravity gravitational wave?
Would it be a mass-carrying gravity gravitational wave?
Is there something inherent in accelerating mass - as was done with the lasing - that will also create a gravity gravitational wave with mass?
Since gravity gravitational waves pretty much pass through everything, what is the "ending state" of these mass-carrying waves? Mustn't we have gravity gravitational waves originating from the Big Bang criss-crossing our galaxy?

I'm not sure what "wave" you're talking about in the second case. The laser beam isn't a gravitaitonal wave.

The usual approximate formula for gravitational radiation (which is a linear approximation) is based on the mass quadrupole. See for instance https://en.wikipedia.org/wiki/Quadrupole_formula.

I have some other answers in posts 3 and 4 in the Physics forum thread https://www.physicsforums.com/threads/gravitational-waves-and-density-of-matter.968868/#post-6153101 that may be of interest. I'll summarize below.

One can simplify the not-very-easy-to-understand quadrupole formula in terms that may be more familiar by using approach mentioned in the text I cited in the above post, MTW's text "Gravitation". This approximation of an approximation relates the power radiated in gravitatioanl waves to the square of the internal power flow. Using standard units, there is a dimensionful constant with units of inverse power with this approach.

However, the internal power flow is assumed to be periodic by the analysis in the above text. I don't think that that would be the case in your example with laser beams, which I don't fully follow.

So this won't necessarily directly answer the question you asked - I'm afraid I don't quite follow the question, and I suspect that if I did, the answer to it would take a fair amount of work to compute.

Note that what Wiki computes, $\bar{h}_{ij}$ is different from what MTW computes (radiated power). What Wiki computes is related to what the gravitational wave instrument (LIGO) measures. The figure for total radiated power is less directly related to the measurment but is of considerable physical interest and may be easier to communicate. If you compare the formula, you may note that the radiated power essentially takes the time derivative of $\bar{h}_{ij}$ and squares it.