|Dec1-12, 11:30 AM||#188|
Notions of simultaneity in strongly curved spacetime
In the case of Schwarzschild spacetime, for example, consider the following three slicings:
(1) The Schwarzschild slicing: slices of constant Schwarzschild coordinate time. Strictly speaking, this is *exterior* Schwarzschild coordinate time, since the "t" coordinate in the SC chart is not timelike for r <= 2m. This slicing only covers the region outside the horizon; the slices actually "converge" as you approach r = 2m, and at r = 2m they all intersect (at least, in the idealized, not physically reasonable case where there is vacuum everywhere--see below under the Kruskal slicing), so the slicing is no longer valid there (you can't have the same event on multiple slices). This is similar to the way Rindler coordinates break down at the Rindler horizon in flat Minkowski spacetime.
(2) The Painleve slicing: slices of constant Painleve coordinate time. This slicing covers the regions outside *and* inside the horizon.
(3) The Kruskal slicing: slices of constant Kruskal time. This slicing also covers the regions outside and inside the horizon; but in addition, it reveals two *other* regions (at least, it does for the idealized, not physically reasonable case where the spacetime is vacuum everywhere, i.e, there is no matter present--in any real spacetime, there would be matter present and the other two regions would not be there) that are not covered by any other slicing.
|Dec14-12, 06:23 PM||#190|
A Mpmentarily Co-moving Inertial Frame is by difinition a limited slice of spacetime. A MOMENT of constant time in the chart of that frame. To say that a MCIF is global is simply false. As far as that goes neither is a Rindler chart global so in fact there is no global chart for an accelerating system in spite of the fact it is moving through flat spacetime. Or do you disagree???
So my statement:
" So harrylin is correct that Adam never crosses the horizon in any MCRF that Eve is at rest in"
unambiguously means that at the moment Eve is at rest in any frame, the charted position of Adam according to the instantaneous metric of this frame is inside the position of the horizon.
Do you still think this is incorrect??
Can you provide an example of a case where this would not apply???
Do you understand that the relevant question is not whether the chart covers the horizon but whether Adam's instantaneous position is inside the horizon's x coordinate or not at the time of evaluation???
But as such still agrees with my statement that there is no significant effect due to Rindler coordinates as opposed to MCRFs . The effects are directly related to acceleration itself and are independent of coordinates.
|Dec14-12, 10:12 PM||#191|
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