PAllen's latest activity
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PPAllen replied to the thread Undergrad Euclidean geometry and gravity.Ok, here I forgot to add 'preserving local density'.
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PPAllen replied to the thread Undergrad Euclidean geometry and gravity.This isn't a good example. To see the issue, you need,e.g. a 'rectangle' bounded by some two value of ##\theta## and r, 'built' far...
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PPAllen replied to the thread Undergrad Euclidean geometry and gravity.Well, it depends on the material model (equivalently, considering e.g. EM fields as well as gravity). A given bound material at some...
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PPAllen replied to the thread Undergrad Euclidean geometry and gravity.Ok, sorry I misunderstood that. This is where I start to differ, and we may never agree. An object is a world tube, and all...
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PPAllen replied to the thread Undergrad Euclidean geometry and gravity.This can't be right. By that logic, you can't embed a 2-sphere in Euclidean 3-space since it has positive scalar curvature and every...
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PPAllen replied to the thread Undergrad Euclidean geometry and gravity.Look later in the paper. They show a wider class of possible born rigid objects when the slices are not flat. But, in any case...
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PPAllen replied to the thread Undergrad Euclidean geometry and gravity.Moving from near flat to more curved, e.g. radial motion SC spacetime.
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PPAllen replied to the thread Undergrad Euclidean geometry and gravity.I found a reference which, indeed claims to show that a rigid body cannot exist in FLRW spacetime with accelerated expansion...
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PPAllen replied to the thread Undergrad Euclidean geometry and gravity.Ok, maybe some sense, but conversely, there is an invariant sense in which you cannot - any such congruence must have changing mutual...
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PPAllen replied to the thread Undergrad Euclidean geometry and gravity.No. See the end of paragraph 2 in irrotational motion in the current Wikipedia article on born rigid motion. Hate to use this, but the...
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PPAllen replied to the thread Undergrad Euclidean geometry and gravity.There is no requirement for constant proper acceleration. Constant position lines in FN coordinates based on a completely arbitrary...
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PPAllen replied to the thread Undergrad Euclidean geometry and gravity.A further nuance is that I think GR may allow a few cases that are not related to KVFs of the spacetime. Consider a stationary rigid...
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PPAllen replied to the thread Undergrad Euclidean geometry and gravity.Having thought about generalizing rigid motion theory from SR to GR, I believe we can all agree on the following for SC spacetime...
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PPAllen replied to the thread Undergrad Euclidean geometry and gravity.Ok, that is fine. However, what is true includes that, in an invariant sense, you can't place the rockets in the new locations at the...
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PPAllen replied to the thread Undergrad Euclidean geometry and gravity.Maybe not. I don’t see why you couldn’t arrange the threads to have no slack in the second case. The threads would just have different...