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This question is a follow-up to the one I asked last week in the thread called, "about tidal forces". In that thread the question came up: what would happen to a sphere of free-falling particles (a "ball of coffee grounds") in a gravitational field described by the Rindler metric? After some analysis the conclusion was reached that - from the perspective of an observer at rest with respect to the Rindler coordinates - the overall shape of the set of particles would change because - as it approached the event horizon - the "top" and "bottom" of the sphere would move closer together.

My question is, since both the Ricci tensor and the Weyl tensor of the Rindler metric are zero, how is it that the size or shape of the sphere changes at all?

I know that the circumstances which create such a situation - being accelerated by, say, a rocket - are not what usually come to mind when one encounters the phrase "gravitational field", and that the spacetime involved is still flat, but my interpretation of the equivalence principle is that a "gravitational field" and an "accelerated frame of reference" should be thought of in the same way.

My question is, since both the Ricci tensor and the Weyl tensor of the Rindler metric are zero, how is it that the size or shape of the sphere changes at all?

I know that the circumstances which create such a situation - being accelerated by, say, a rocket - are not what usually come to mind when one encounters the phrase "gravitational field", and that the spacetime involved is still flat, but my interpretation of the equivalence principle is that a "gravitational field" and an "accelerated frame of reference" should be thought of in the same way.

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