PAllen's latest activity
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PPAllen replied to the thread I Missing proof of the Shell theorem in General Relativity.You assume nothing but spherical symmetry, and vacuum outside some r. You assume nothing about inside r (except spherical symmetry...
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PPAllen replied to the thread I Missing proof of the Shell theorem in General Relativity.Never intended to imply that. Adjusted the wording slightly, hopefully for the better ...
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PPAllen replied to the thread I Missing proof of the Shell theorem in General Relativity.Up to the stability issue raised by @PeterDonis (Buchdahl's theorem), there are many sources that prove this, even in, e.g. the case of...
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PPAllen replied to the thread I Missing proof of the Shell theorem in General Relativity.Ok then it would be easy to provide one. For example, I have about 10 GR texts, spanning publication dates from 1921 to 2015. All derive...
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PPAllen replied to the thread A Question on Dirac's derivatives of the 4-velocity w.r.t. coordinates.Except that in a few lines they derive your first equation from the field form, so, no, you don’t need any extra computation, nor do you...
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PPAllen replied to the thread A Question on Dirac's derivatives of the 4-velocity w.r.t. coordinates.But this is correct - the covariant derivative operator is only defined for a field, and the first of these is the component notation...
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PPAllen replied to the thread A Question on Dirac's derivatives of the 4-velocity w.r.t. coordinates.That's not what I am talking about. In section 10.4, in equations 10.20 and 10.21, MTW introduce what other authors call the absolute...
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PPAllen replied to the thread A Question on Dirac's derivatives of the 4-velocity w.r.t. coordinates.Note also, that Wald does derive, in passing, that parallel transport along a curve ends up depending only on values along the curve...
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PPAllen replied to the thread A Question on Dirac's derivatives of the 4-velocity w.r.t. coordinates.Note, reviewing section 10.4 of MTW, I don't see any imprecision. Here, the absolute derivative (without using that name) is introduced...
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PPAllen reacted to PeterDonis's post in the thread A Question on Dirac's derivatives of the 4-velocity w.r.t. coordinates with
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More precisely, he defines geodesics in terms of the derivative operator ##\nabla_a##, which he defines earlier, in Section 3.1, as an... -
PPAllen replied to the thread A Question on Dirac's derivatives of the 4-velocity w.r.t. coordinates.Wald, so far as I can see, only deals with cases where a field is given, and the covariant derivative is what is desired. However, they...
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PPAllen replied to the thread A Question on Dirac's derivatives of the 4-velocity w.r.t. coordinates.I also don't like the confusion in many physics oriented presentations of the concept of absolute derivative along a curve versus...
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PPAllen replied to the thread A Does the EP imply that a free-falling observer follows a geodesic?.Looking at the link in the OP, the cited reference is using a different definition of the strong equivalence principle than other...
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PPAllen replied to the thread A Covariant form of Maxwell's (inhomogeneous) equations (in GR).The main discussion is in and around box 16.1, p. 390 of my edition.
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PPAllen replied to the thread A Covariant form of Maxwell's (inhomogeneous) equations (in GR).MTW has discussion of the subtleties and physical basis of the comma to semicolon rule, including cases where it fails. Ultimately, you...