Science > Physics > Derivative Products of Form (df/dx)(dg/dx) in Physics 7: Gravitational Electrodynamics, Metrics
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Science > Physics |
| User: |
"OsherD" |
| Date: |
08 Jan 2006 08:58:07 PM |
| Object: |
Derivative Products of Form (df/dx)(dg/dx) in Physics 7: Gravitational Electrodynamics, Metrics |
From Osher Doctorow
A. B. Balakin et al, "Radio wave 'messengers' of periodic gravitational
radiation and the problem of gravitationally induced nonlinearity in
electrodynamic systems," gr-qc/0511053 v1 10 Nov 2005, obtain the key
equation (p. 3):
1) Du(A) = (1/2)Q(R_.u3u)^3 U_2 exp(-b) Dv(A)[U_u Dv(A) + Uv(Du(A) - b'
A)] + phi(u)
which for the second bracketed term has a generalization of
(df/dx)(dg/dx) with respect to u and v with Du, Dv covariant
derivatives. A is the vector potential describing the electromagnetic
field, A_i = delta_i ^3 exp(-b) A(u, v), U_i is the velocity vector.
A second direction in which (df/dx)(dg/dx) generalizations are
important is the metric for Riemannian geometry and the metric for
Finsler geometry via dx^i dx^j terms with i not equal to j or
"trivially" with i = j. Finsler geometry is more general in the form
of the metric, but includes Riemannian geometry as a proper subset.
Osher Doctorow
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| User: "Fusar Gramin" |
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| Title: Re: Derivative Products of Form (df/dx)(dg/dx) in Physics 7: Gravitational Electrodynamics, Metrics |
10 Jan 2006 08:49:10 AM |
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"OsherD" <> wrote in message
news:1136775487.214416.219330@f14g2000cwb.googlegroups.com...
From Osher Doctorow
A. B. Balakin et al, "Radio wave 'messengers' of periodic gravitational
radiation and the problem of gravitationally induced nonlinearity in
electrodynamic systems," gr-qc/0511053 v1 10 Nov 2005, obtain the key
equation (p. 3):
1) Du(A) = (1/2)Q(R_.u3u)^3 U_2 exp(-b) Dv(A)[U_u Dv(A) + Uv(Du(A) - b'
A)] + phi(u)
which for the second bracketed term has a generalization of
(df/dx)(dg/dx) with respect to u and v with Du, Dv covariant
derivatives.
No it is not. I see a + sign between the terms, kosher.
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| User: "OsherD" |
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| Title: Re: Derivative Products of Form (df/dx)(dg/dx) in Physics 7: Gravitational Electrodynamics, Metrics |
08 Jan 2006 09:06:42 PM |
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From Osher Doctorow
The full list of authors is A. B. Balakin, G. V. Kisun'ko, and Z. G.
Murzakhanov (Kazan State U. Russia for the first and third authors,
Russian Academy of Sciences for the third author).
The phi(u) term can be eliminated by an appropriate (initial) condition
on the hypersurface v = 0.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Derivative Products of Form (df/dx)(dg/dx) in Physics 7: Gravitational Electrodynamics, Metrics |
08 Jan 2006 09:11:00 PM |
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From Osher Doctorow
The full list of authors is A. B. Balakin, G. V. Kisun'ko, and Z. G.
Murzakhanov (Kazan State U. Russia for the first and third authors,
Russian Academy of Sciences for the third author).
The phi(u) term can be eliminated by an appropriate (initial) condition
on the hypersurface v = 0.
Osher Doctorow
.
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