PAllen's latest activity
-
PPAllen replied to the thread I Euclidean geometry and gravity.Ok, here I forgot to add 'preserving local density'.
-
PPAllen replied to the thread I 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...
-
PPAllen replied to the thread I 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...
-
PPAllen replied to the thread I 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...
-
PPAllen replied to the thread I 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...
-
PPAllen replied to the thread I 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...
-
PPAllen replied to the thread I Euclidean geometry and gravity.Moving from near flat to more curved, e.g. radial motion SC spacetime.
-
PPAllen replied to the thread I 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...
-
PPAllen replied to the thread I 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...
-
PPAllen replied to the thread I 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...
-
PPAllen replied to the thread I Euclidean geometry and gravity.There is no requirement for constant proper acceleration. Constant position lines in FN coordinates based on a completely arbitrary...
-
PPAllen replied to the thread I 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...
-
PPAllen replied to the thread I 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...
-
PPAllen replied to the thread I 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...
-
PPAllen replied to the thread I 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...