Re: E. Noether contra B. Carter

On Sat, 21 Sep 2024 6:01:55 +0000, The Starmaker wrote:

The Starmaker wrote:

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JanPB wrote:

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On Thu, 19 Sep 2024 7:31:58 +0000, The Starmaker wrote:
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JanPB wrote:

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[...]

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Your math is correct but doesn't seem to have any meaning.

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No geometric meaning (which I was hoping for).

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i see, you have your own approach to doings things no one else does..

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Also the P isn't standard and needs more clarification

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K = < r^2 gamma' - rho^2 P(gamma') , gamma' >

OK, fair point.  Surprisingly perhaps, the Kerr spacetime has
an orthogonal moving frame almost everywhere (away from the
usual suspects like the singular set and the horizons):
    e0 = (r^2 + a^2)@/@t + a @/@phi
    e1 = @/@r
    e2 = @/@theta
    e3 = a sin^2(theta) @/@t + @/@phi
e2 and e3 are always spacelike while  e0, e1  are always of
the opposite causal character, so  e0  and  e1  span a
Minkowski signature plane, called the principal plane.
The  P  I used above denotes the orthogonal projection onto
that plane.
BTW, a geodesic is called principal if its tangent vector
lies in the principal plane.
EXERCISE. Let  gamma  be a timelike geodesic.  Then:
    K = 0  if and only if  gamma  is a principal in
    the equatorial plane (theta = pi/2).

further more, there are too many errors for me to list them all...

There are no errors.

you finally reached ...kooksville.

Talk is cheap.
--
Jan