Could a planet orbit a gravitational wave concentration

Question

So say many light years away there are many black holes colliding and so there are many 9 solar mass gravitational waves floating around and some of them concentrate around a 10 earth mass planet. So what would happen if some of that concetrated near the planet, would the planet be pulled towards this concentration and then start orbiting the gravitational wave.

Also what happens if a 10 earth mass planet with radius of 10 earth radii, has 1 solar mass gravitational wave passing through the planet?Would the planet collapse into a white dwarf and then quickly expand as the wave leaves the planet heating up in the process?

Answer 1

No. (at least not in the way you imagine)

The requirement for something to orbit is a region of space with positive curvature. The curvature can be determined from the "stress energy tensor" and so you need a region of space with a concentration of "energy". But the only practical way the universe has of concentrating that much energy into a small space (so that something can orbit it) is the "frozen" form of energy that we call "mass".

Now there is a thing called a "kugelblitz", it is a black hole made of light. If you get enough light energy into a small enough region of space, the energy of the light will cause space to curve and create a black hole. That black hole will be indistinguishable for any other black hole, and things could orbit it. Now gravitational waves also carry energy, so if you focussed enough gravitational waves into a small region of space, you could create a gravitational kugelblitz, which would be a black hole formed of gravitational radiation, and you could orbit it. It would be exactly like any other black hole.

But don't get your hopes up. Kugelblitz are completely theoretical, as nobody has anything like the practical ability to focus light into a sufficiently small region of space. And gravitational kugelblitz are far far harder to create than one made of light. There is no practical way of focussing gravitational waves. Those produced by a black hole merger just spread out. It wouldn't be practically possible to produce enough gravitational waves that overlap to create a black hole.

And anyway this isn't a planet orbiting a wave, it is just a planet orbiting a black hole.

Gravitational waves produced from merging black holes spread out, they aren't beamed, and aren't confined to a planet sized region of space. There isn't an astrophysical process that can create a pulse of gravitational waves in a narrow beam, so its just not possible to get a solar mass of gravitational wave energy inside a planet. (but god help planet if you did, the stress would be immense)

Gravitational waves don't act like "tractor beams". As the pass matter is stretched and compressed, deforming circles into ellipses. It doesn't cause matter to get pulled together. They can't cause gravitational collapse. They don't make the planet smaller or form a white dwarf or anything like that.

So the simple answer to your question is "No".

Answer 2

Gravitational waves move at the speed of light, so one cannot orbit a gravitational wave packet - simply because one cannot keep up.

One might also imagine a lot of waves passing through a smaller region like the beam waist of a Gaussian electromagnetic wave, and indeed there is a gravitational counterpart to the Gaussian beam. Unfortunately the model only works for weak gravitational waves, so it does not give any evidence for being able to make anything attractive (the field outside the waist is essentially zero for the weak waves).

John Wheeler suggested in 1955 that maybe gravitational waves could form strongly bound systems carrying mass, "geons". These structures appear possible mathematically, but unfortunately they do not appear to be stable. It does not look likely one could orbit gravitational waves unless they are strong enough to collapse into a black hole.

Generally, the coupling of gravitational waves to matter is so small that even a solar mass gravitational wave will pass by invisibly unless one is very close (within 100 Schwarzschild radii) to the source.

Answer 3

The answer is likely no. I have not seen the math to show that gravitational waves could constructively interfere into a clump as opposed to a cylindrically symmetric wave, but even if some local pocket of non-symmetric gravitational waves did manifest, it would be moving at the speed of light, and for any planet to even partially orbit it itself would have to coincidentally be moving near the speed of light at the exact right angle tangential to the wave. Since the planet itself cannot move at the speed of light, this is guaranteed to be an unstable system anyway, and the relativistic potential mathematically cannot form a closed orbit.

As per your second question, no the planet would not collapse into a white dwarf, it would simply become denser and hotter, planets already are held up by electron degeneracy pressure. If that's all you mean by a white dwarf, then planets are already white (technically black) dwarfs. And regardless, gravitational waves do not spherically compress objects they move through, they compress the object in one direction and expand it in an another, both orthogonal to the direction of the wave's travel.