On 7/23/2020 7:33 AM, Alan Grayson wrote:
On Thursday, July 23, 2020 at 8:27:52 AM UTC-6, Lawrence Crowell wrote:
Coordinates are not the basis of physics. Curvatures are
covariant, while connections and coordinates are not. These can be
imposed in many ways, similar to a gauge choice.
LC
That right; coordinates are not the basis of physics. That's why
Einstein had to cast his GR equation in tensor form, so the laws of
physics would be independent of coordinate systems. But you're
asserting, or so it seems, that there is a unique coordinate system
wherein the external gravitational effect of a BH can be calculated.
This is what I object to. AG
Calculations are always done in some coordinate system. The method is
to calculate something, like the curvature tensor or a proper time, that
doesn't depend on which coordinate system you used.
Brent
On Thursday, July 23, 2020 at 6:49:44 AM UTC-5 [email protected]
wrote:
On Thursday, July 23, 2020 at 5:41:42 AM UTC-6, Lawrence
Crowell wrote:
On Thursday, July 23, 2020 at 5:56:32 AM UTC-5
[email protected] wrote:
On Saturday, July 18, 2020 at 6:31:23 AM UTC-6, Alan
Grayson wrote:
On Saturday, July 18, 2020 at 6:18:28 AM UTC-6,
Lawrence Crowell wrote:
The tortoise coordinates is found from the
Schwarzschild metric
ds^2 = (1 - 2m/r)dt^2 - (1 - 2m/r)^{-1}dr^2 -
r^2dΩ^2
where for a signal leaving a point near the
black hole with ds = 0 (null path) and
propagating radially out, dΩ = 0, we have dt =
dr/(1 - 2m/r) which then leads to
T = t - t0 - 2m ln|r - 2m|.
That is the tortoise coordinate. Please look
this up to read further. I can't spend
beaucoup time going over this for weeks to come.
LC
You don't have to. We're done. But you should IMO
address Brent's objection, maybe on another thread. AG
When it comes to GR, you're a genius; no question
about it. I wouldn't want to waste your valuable time.
But consider this; the Schwartzschild metric applies
to NON-ROTATING masses. Do you really think a massive
contracting star which forms a BH will be
non-rotating? Obviously, it will be RAPIDLY rotating,
like an ice skater who contracts her arms. Brent also
had some substantive questions about your model. But I
see you prefer your illusions than to address his
objections. AG
The result is similar, but more complex. The same
calculation can be done for the Kerr solution. It is just
a lot more complicated mathematically.
LC
If you say so. In any event, the idea that an objectively
existing gravitational field outside a BH should depend on the
choice of a particular coordinate system, seems a non-starter. AG
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