[2/4] You toss a ball straight up. As it rises, it veers sideways, and it lands over to your left — as if the habitat were spinning along an axis that passed through the floor, and the Coriolis force sent the ball askew. But … the stars aren’t moving! The only explanation is
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[3/4] that the habitat is hovering above a rotating black hole — not orbiting the hole, but using its engines to stay put. It’s not rotating with respect to infalling starlight — but it *is* rotating relative to the definition of “non-rotating” built into the local spacetime.
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[4/4] Fine print: alas, *no* choice of black hole mass M, black hole rotation, and distance R from the hole could make the distance the ball swerved visible to the naked eye, if weight is 1 gee. Frame dragging per se can be made arbitrarily large, but: ω < g / [c (R/M–1)]
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I inadvertently used a mix of conventional units (ω, g and c) and geometric units (R and M). In geometric units, G=c=1, and mass and distance have the same units, so R/M is dimensionless. I should have written: ω < g / [c (2R/R_s–1)] R_s = 2GM/c^2
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Any rotating mass has a frame-dragging effect, right? Is there a difference between black holes and other bodies (except magnitude of the effect)? https://en.wikipedia.org/wiki/Gravity_Probe_B …
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Right. No difference.
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I think the part that my mind refuses to grasp isn't so much that the BH can change what "rotating" means in the surrounding spacetime, but that it levels off - you can't just draw a straight line out and assume an object that far away would also be subject to the same forces
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