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| Author |
Message |
| Barrow |
 Posted: Thu Dec 28, 2006 12:44 pm |
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Guest
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Dear all,
The book talking about Relativistic Chaos says: The Einstein
equations is a nonlinear partial differential equations with "infinite
number of degrees of freedom." The cosmological principle reduces the
gravitational degrees of freedom to one(the cosmological scale factor)
in Friedmann-Roberson-Walker cosmology.
My problem is, how come there are infinite number of degrees of
freedom??? Isn't there 10 independent field equations? (G_{\mu\nu} = 0
for vacuum) Isn't there 10 independent components for the metric
tensor??(g_{\mu\nu}) So the degree of freedom is at most 10. Where am I
wrong??
By the way, one more question, how can I tell the field equations are
independent or not? Because the field equations of Bianchi-IX for scale
factors a(t), b(t) and c(t) are R_{11} = 0, R_{22} = 0, R_{33} = 0 and
R_{00} = 0, and the four field equations are not independent since
there are only 3 independent variables.
Thanks for your help! Sincerely Barrow |
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