I'm puzzling over a certain aspect of the interpretation of frame-dragging.(adsbygoogle = window.adsbygoogle || []).push({});

Frame-dragging says that the angular momentum of a body makes itself felt in a certain way in the curvature of the spacetime surrounding it. In GR, you typically can't point to a certain spacelike surface with a boundary around it, and say, "The amount of angular momentum inside the boundary is x." This only becomes possible under certain assumptions, e.g., asymptotic flatness. MTW have a nice argument to this effect, which is that in a closed universe, the boundary has two sides to it, so the flux of some quantity passing through the boundary cannot unambiguously be attributed to either of the two regions on the two sides.

In an experiment to detect frame-dragging, it therefore seems to me that you must carry out some measuring operations that depend on asymptotic flatness. For example, you could build two gyroscopes A and B out in the flat region, then carry A in close to the rotating body, loop it around once in the equatorial plane, and then transport it back out to the flat region and compare it with B. Call this experiment #1.

On the other hand, suppose you have two satellites, C and D, one in a prograde equatorial orbit and one in a retrograde orbit. Frame dragging causes them to have different orbital periods, and I think this is *locally* measurable. E.g., you can have the satellites depart from a certain starting point in opposite directions, then reunite on the other side, and I think you would see a different amount of proper time on their clocks. Call this experiment #2.

In practical terms, Gravity Probe B has verified frame-dragging to 15%. It used a distant star as a reference point, so it certainly wasn't carried out entirely locally.

The interpretation that I'm thinking is correct is that although experiment #2 is purely local, in a universe without asymptotic flatness the results can't be interpreted unambiguously as a measurement of the angular momentum contained *inside* the orbit. Is this correct?

TIA! -Ben

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# Local detectability of frame-dragging

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