Gravitational waves inside the Earth(or similar object)

[Genady]

Just now, geordief said:

Perhaps irrelevant but did Einstein state this or did he perhaps just state that they were indistinguishable with the qualification coming some time later?

 

It always was so in GR. It was so in Riemannian geometry as well, in the form of any manifold being indistinguishable from a flat surface in infinitesimally small neighborhood of a point.

[geordief]

2 hours ago, geordief said:

So ,if there  are very small accelerations in a system  which do not produce gravitational  waves do they have any  gravitational effect at all ?

I understand that in the frame of the accelerated objects  acceleration is indistinguishable  from gravity - but (as per @joigus) this is not a  frame independent effect.

 

So can I take it that there are no gravity related effects from any accelerated motion,specifically  that there is no effect on the gravity field?

@swansont please ignore  this. I think I understand that point now(ie there is a gravitational effect but not necessarily or in any likelihood any gravitational waves)

[swansont]

2 hours ago, geordief said:

Perhaps irrelevant but did Einstein state this or did he perhaps just state that they were indistinguishable with the qualification coming some time later?

It’s a practical issue. A real gravitational system doesn’t have uniform acceleration, since it would be radial from a point. The direction would vary a small amount over any finite tangential extent

[Markus Hanke]

9 hours ago, geordief said:

Could you explain a little further about that? (or would it be  easyish  for me to look that up on google?)

Perhaps an illustration would help to clarify the difference between “dipole” and “quadrupole”.

In the following, the two black dots in the middle move only vertically, i.e. up-down - so there’s only two “poles” (hence dipole), being the top and the bottom. Like so:

https://en.wikipedia.org/wiki/Dipole#/media/File:Electric_dipole_radiation.gif

On the other hand, the following shows a situation where the system oscillates up-down and left-right. Here you have four “poles”, being top, bottom, left, right. Hence quadrupole. It’s essentially a combined system of two dipoles.

https://en.wikipedia.org/wiki/Gravitational_wave#/media/File:GravitationalWave_PlusPolarization.gif

EM radiation is at least dipole, e.g. electrons oscillating up and down in an antenna will generate electromagnetic waves. Gravity requires at least a quadrupole in order to generate gravitational radiation - a system that has only a dipole moment is not enough. 

Does this make sense?

[geordief]

4 hours ago, Markus Hanke said:

Perhaps an illustration would help to clarify the difference between “dipole” and “quadrupole”.

In the following, the two black dots in the middle move only vertically, i.e. up-down - so there’s only two “poles” (hence dipole), being the top and the bottom. Like so:

https://en.wikipedia.org/wiki/Dipole#/media/File:Electric_dipole_radiation.gif

On the other hand, the following shows a situation where the system oscillates up-down and left-right. Here you have four “poles”, being top, bottom, left, right. Hence quadrupole. It’s essentially a combined system of two dipoles.

https://en.wikipedia.org/wiki/Gravitational_wave#/media/File:GravitationalWave_PlusPolarization.gif

EM radiation is at least dipole, e.g. electrons oscillating up and down in an antenna will generate electromagnetic waves. Gravity requires at least a quadrupole in order to generate gravitational radiation - a system that has only a dipole moment is not enough. 

Does this make sense?

Yes,thanks.I think that explanatory  visualization  was around at the time when the first gravitational  waves  were detected some years ago.

@swansont explained you needed a "dumbbell" shape to produce the waves,I think and @joigus said that you only got g-wave emissions in extraordinary large systems comparable to the big bang  although he did  mention the gravitomagnetic phenomena that I think are yet to be detected experimentally.

I have read a few comments elsewhere about the possibility of engineering micro black holes but  it is just the odd comment I have seen and I think we may see  cheap fusion power before they get around to marketing diy g-wave kits</sarc>

[Markus Hanke]

1 hour ago, geordief said:

you only got g-wave emissions in extraordinary large systems comparable to the big bang

It doesn’t have to be on the scale of the BB. In practice, any binary pair of massive enough compact objects will emit (currently) detectable G-radiation - examples would be binary neutron stars, or binary black holes. Also the merger of such objects (and, in the case of black holes, the ring-down phase afterwards) will be a G-wave emitter. I would hazard a guess and say that our G-wave detectors will become more sensitive as time goes by, so eventually we should also be able to detect the gravitational signature of less massive things, like ordinary binary stars. But I think we are very far away from being able to detect anything much smaller than that (like eg oddly-shaped planetary bodies).