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this post was submitted on 15 May 2025
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Oh that makes sense. I though it was space time itself which was moving, bringing with it the objects on it. (probably had seen some illustration representing it like that)
But yes the gravitational waves take is interesting, it burn my mind trying to imagine how to "trap" spacetime in itself.
It's "just" curvature, both through space and time. The Einstein field equation literally has energy and momentum on one side, and a type of curvature measure on the other.
The trick there is that curved 2D spaces can already be pretty weird, and it gets exponentially crazier in dimensions 3 and 4. This makes it both capable of doing surprisingly a lot, like putting Earth in a fixed, repeating orbit without much local distortion, and difficult to visualise even by analogy. Interestingly, dimensions 5 and higher aren't any worse, which is actually a pattern that repeats across a lot of geometry.
In slightly more mathy detail:
A curved 2D surface can be completely characterised by the Gaussian curvature at each point, which is a single real number (aka a scalar). In dimension 3, you need to use the Ricci curvature, which is a 3x3 matrix/tensor, so 9 scalars, and in dimension 4 it's the Riemann curvature tensor which is 4x4x4x4. There's symmetries that you can use to get that down to 6 and 20 scalars respectively, but that's still a lot more parameters on every point than we're used to.There is a bit of nuance there, which is why I said "as I understand it". Gravitational waves are classically defined in terms of perturbations of flat spacetime, and a black hole is nowhere near close to flat. It's possible there's been work showing how to define them in that context, but I'm not a specialist and I couldn't name it.
If this were electromagnetism I'd just use the superposition principle, but GR is not linear. In fact, there's chaotic dynamics that can happen in black holes related to the Mixmaster universe model. It's also possible (to my limited knowledge) that there isn't nice propagating waves at all so much as just adjustments to the crazy bending everything is already doing.