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What is a definition in GR that correctly captures the concept that a frame is rotating? Is it enough to say that it's stationary but not static?
atyy said:There is a definition of rotating for a family of observers. Roughly, if they are not rotating, then there is space at a time for them (or something like that). Try Eq (2.3.5) and (2.3.6) of Eric Poisson's http://www.physics.uoguelph.ca/poisson/research/agr.pdf.
I don't think this works, because by the equivalence principle a centrifugal force is equivalent to a gravitational force.edpell said:One observes no fictitious centrifugal force. ?
bcrowell said:Thanks for the link, atyy! Hmm...I think what he's saying with the timelike congruences is essentially equivalent to the idea that a particular observer can check whether the Sagnac effect exists. For instance, say you have a rotating disk. You can make a timelike congruence consisting of world-lines at rest relative to the axis, or a congruence consisting of world-lines at rest relative to the disk. In the latter case, you get a Sagnac effect at every point in space.
I guess my question was awfully vague, but this may help to point me in the right direction to make it more well defined. It seems straightforward to define the right notion for a local observer: do you get a Sagnac effect? I had in mind more the question of whether there was any way to say anything globally.
atyy said:And somehow the Sagnac effect links both of them, and they also say rotation is only a "local" concept in GR. I haven't read the paper beyond that.
A rotating frame in General Relativity (GR) refers to a coordinate system in which the laws of physics are described in terms of a rotating observer. This frame is used to study the effects of rotation on objects in spacetime, such as the frame-dragging effect predicted by GR.
A rotating frame is non-inertial, meaning that it is accelerating or rotating with respect to an inertial frame. This results in the appearance of fictitious forces, such as the Coriolis and centrifugal forces, which do not exist in an inertial frame.
In GR, rotating frames are used to study the effects of rotation on spacetime, particularly in the presence of massive objects. This is important for understanding phenomena such as frame-dragging and the behavior of spinning black holes.
The Equivalence Principle states that the effects of gravity are indistinguishable from the effects of acceleration. In a rotating frame, the acceleration due to rotation can be considered equivalent to the gravitational force, allowing for the study of gravitational effects in rotating systems.
One example of a rotating frame in GR is the Frame-Dragging Experiment (FRE) conducted by NASA, which used a satellite to measure the frame-dragging effect of the Earth's rotation on nearby space. Another example is the study of the Lense-Thirring effect, which describes the rotation of spacetime caused by a rotating massive object.