Recent content by PeterDonis

Not really. In polar coordinates the metric coefficient ##g_{rr}## vanishes at ##r = 0##. That means the metric has a vanishing determinant, but it doesn't make it undefined. In Schwarzschild coordinates, the metric coefficient ##g_{rr}## is undefined at ##r = r_s## (zero in the denominator)...

No, it's the overall blueshift, period. The +45 is the "gravitational" part and the -7 is the "motion" part. (Note that, as @JT Smith pointed out, these should be microseconds per day.) The split between "gravitational" and "motion" is frame-dependent; those numbers are for the ECI frame. The...

From post #14 it looks like it is.

That's true, but more importantly, you still haven't told us what reference this is from or given a link to it. We can't comment on quotes from a reference we don't know.

No. "Created out of nowhere" would violate the local conservation of stress-energy. Any viewpoint that says the "total energy contained in dark energy" is increasing has to make use of some global quantity that is not a tensor and has nothing to do with the local conservation law.

While this is true, it is also true that there will be cases where doing this will end up with something that isn't "what people generally mean" about that specific spacetime. For example, if you want a chart with these properties on Schwarzschild spacetime including the black hole region, you...

Yes. Yes. (But note that it should be ##\partial_T## in the quote above, since I was using ##T## for the Painleve time coordinate.)

It involves a functional derivative with respect to the function that is the derivative with respect to ##x^\beta## of ##A_\alpha##. The Lagrangian is a functional of that function (as well as of the function ##A_\alpha## itself, considered as a function on spacetime). It's possible that...

Where did you get that from? You need to give a reference.

Per my post #7 just now, this equation isn't even well-defined. Where are you getting it from?

That expression isn't even well-defined. ##g_{\sigma \tau, \beta}## means ##\partial / \partial \beta ( g_{\sigma \tau} )##. You can't take a derivative with respect to that. If the OP is trying to do that, the OP is trying to do something that isn't well-defined.

Perhaps so, but in any event that is not the standard interpretation of time zones. Nobody actually treats 9 am Eastern and 9 am Central as simultaneous. Everybody understands that the latter is an hour later than the former. So if he is claiming that his proposal is just like the standard usage...

Thread closed for moderation.

Yes, we discussed that before. To recap briefly, time zones and dates don't define a foliation that has timelike tangent vectors on its simultaneity surfaces. They just define different labelings of a foliation whose simultaneity surfaces are all spacelike. For example, if I adjust my clock from...

I agree that this case (timelike integral curves, spacelike foliation surfaces) will be the one that most clearly matches our intuitive sense of how things should work, and is therefore the most "natural" case.