On Mon, 5 Jan 2009 22:58:52 -0800 (PST), Koobee Wublee
wrote:
On Jan 5, 10:37 pm, George Hammond wrote:
Koobee Wublee wrote:
Whether you know what asymptotically flat means or not, it still
remains your problem. shrug
Strictly speaking "asymptotically flat" means the 4th
order Riemann curvature tensor goes to zero at r=infinity.
In simple cases this can be determined by inspecting the
metric.... if it approaches the Minkowski metric for r=oo
then the space is asymptotically flat. For instance the
Schwarzchild metric approaches the Minkowski Metric in
spherical coordinates for r--oo.
It actually does not involve the Rieman curature tensor.
[Hammond]
Nope... it actually does.
As long as
the geometry approaches flat space at r = infinity, it is considered
asymptotically flat.
[Hammond]
That's a tautology not a definition.
Both spacetimes I have described below satisfy
this criterion. shrug
[Hammond]
Of course they do since they are both identically the
Schwarzchild Metric. Shouldn't you be getting back to the
shop?
** ds1^2 = c^2 (1 – K / r) dt^2 – dr^2 / (1 – K / r) – r^2 dO^2
** ds2^2 = c^2 dt^2 / (1 + K / r) – (1 + K / r) dr^2 – (r + K)^2 dO^2
[Hammond]
I'll give you a clud Kooby.... really smart people don't
challenge Relativity.... they discuss how Relativity
explains God, even Einstein couldn't figure that out.
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