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How can you change space-time? It's already got a time dimension, so you'd need another time dimension with respect to which to take the derivative. Or is the real claim here that gravitational waves distort space as part of their temporal dynamics?

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We already know that spacetime has local curvature, so it’s possible that spacetimes curvature isn’t static. How this affects or interacts with time isn’t clear, since we don’t really understand what spacetime is or how it comes to be.

I think if both of you aren't aware, this talk on the concept of time orientability might be interesting exploration on this: https://yewtu.be/watch?v=Mk7vkhT0UCM

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