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Frame-dragging deforms spacetime around a rotating spherical, isotropic distribution of matter (the distribution doesn't change in time). The spacetime is a little bit dragged away from the Schwarzschild metric belonging to the same but non-rotating distribution.
Now, a spacetime surrounding such a distribution of matter is said to be stationary. The spacetime is invariant when translated in time, but not when time inversed, in which case the spacetime is dragged in the other direction (which makes, loosely speaking, the difference with a static spacetime). I was under the impression though that spacetime around such a rotating distribution, is dragged along somewhat like the spring of an old-fashioned alarm clock is dragged along. That is, I thought that space is stretched slowly and continuously in a direction for which $r$ (the distance to the center of the distribution) is fixed. Which would mean that you could determine the age of the Earth by looking at the metric around the Earth. Am I wrong (I'm almost certain I am but not entirely)? And am I right in saying that frame-dragging isn't caused by mass but by the velocity of mass (momentum)?

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  • $\begingroup$ The teaching problem here is increased by the fact that "frame dragging" is a poorly-chosen term for the effects on spacetime associated with rotating bodies. The two main effects are that inertial frames near a rotating body are in a state of rotation relative to the distant universe, and there are no purely radial timelike geodesics in an ergosphere. $\endgroup$
    – Andrew Steane
    Commented Dec 22, 2023 at 13:46

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It sounds like you're thinking of frame dragging as a literal process where spacetime is "wrapped" around the Earth. That's not really a good picture. Your later comment about it being caused by momentum is more accurate: any rotating body has angular momentum, and this contributes to the stress-energy tensor which causes spacetime curvature. This is "continuous" in the sense that as long as it is present it has effects on the curvature of spacetime, but it isn't cumulative. It doesn't keep building up more and more, it's just a fixed contribution to spacetime curvature which causes an asymmetry (different curvature) in the direction of rotation.

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  • $\begingroup$ This is exactly what I meant! $\endgroup$
    – Deschele Schilder
    Commented May 17, 2021 at 23:30

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