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From: film.art@gmail.com (JanPB)
Newsgroups: sci.physics.relativity
Subject: Re: E. Noether contra B. Carter
Date: Sun, 22 Sep 2024 16:18:11 +0000
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On Sat, 21 Sep 2024 6:01:55 +0000, The Starmaker wrote:

> The Starmaker wrote:
>>
>> JanPB wrote:
>>>
>>> On Thu, 19 Sep 2024 7:31:58 +0000, The Starmaker wrote:
>>>
>>> > JanPB wrote:
>>> >>
>>> [...]
>>> >
>>> > Your math is correct but doesn't seem to have any meaning.
>>>
>>> No geometric meaning (which I was hoping for).
>>
>> i see, you have your own approach to doings things no one else does..
>
>> Also the P isn't standard and needs more clarification
>
> 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