(Ken S. Tucker) wrote in message . com...

I GOOFED MAYBE...

My post on 09-16 09:28 to this thread contains an error,
please forgive.

Hi Perion (this is my second post to your reply)
I studied the first part of gr-qc0207/0207065, and using
this ref. I can be very specific about my apphrensions,
which anyone can kindly check and correct.

For brevity I'll sub Eq.(10) into (8) and write this,

h^0i = S^n x^k e^i_nk [-2*G/c^3r^3] Eq.8(10)

e^i_nk is Levi-Cevita's antisymetrical tensor and
the stuff in [] is not germain, latin indices are summed
over 1,2,3.

Eq.8(10) supposedly transmits the information about
the rotating source mass to the field, including
rotation direction information.

I find h^0i =0, here's why...
(( ERROR ))

1) I implicitly assume S^n x^k = x^k S^n,
because the notation implies an outer product.

2) I assume summation over indices 'n' and 'k',
as they are repeated twice in the same term.

3) I assume the permutation e^i_nk = - e^i_kn.

So if we arbitarily set i=1, and []=1 then sum,

h^01 = S^2 x^3 e^1_23 + S^3 x^2 e^1_32

and because e^1_23 = - e^1_32,

the CORRECTED substitution for Eq. 8(10) is,

h^01 = S^2 x^3 - S^3 x^2.

But that can't work either, because we're setting

Symmetrical (0,1) = Antisymmetrical(2,3)

I think the Levi-Cevita tensor requires 4 indices
in space-time, however Eq. 8(10) has only 3.
In 4D one requires, e_uvab where indices u,v,a,b
can take on any dimension 0,1,2,3.

Apart from this problem, it seems impossible to
encode rotation direction information - which
requires asymetry - into the symmetrical
component h^0i.

Regards
Ken S. Tucker