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Re: Does Velocity Play A Factor?

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Posted by me on November 14, 1999 18:08:48 UTC

That the Riemann tensor (not curvature tensor) does not vanish is irrelevant. - I disagree. Spacetime curvature and tidal gravity are the same thing. Mathematically, the curvature tensor (i.e. the Riemann tensor) can be calculated directly from the tidal force tensor. Thus local (i.e. infinitely small) measurements of tidal force can be used to determine the curvature tensor. If the tidal force tensor vanishes then the curvature tensor vanishes. However the existence of curvature is an invariant property of spacetime so the tidal force tensor cannot vanish. Any body of finite size will be subject to tidal distortions even in locally inertial frames. Locally inertial means that the metric, guv, is the Minkowski metric nuv. So in a locally inertial frame guv = nuv. But this does not imply that that curvature tensor vanishes. This also implies that the tidal force tensor does not vanish. In fact an observer in orbit around a black hole will feel the tidal forces. Even if the observer is very small e.g. 10 cm.

Since the question regarded the distortion of objects it is assumed that the object is not a point particle.

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