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Spherically symmetric metric in isotropic coordinates ?

  1. Apr 2, 2008 #1
    spherically symmetric metric in isotropic coordinates ???

    The most general spherically symmetric metric can be written as:

    [tex] ds^2 = - dt^2 + X^2(r,t) dr^2 + R^2(r,t) (d\theta ^2 + sin^2(\theta) d\phi^2) [/tex]

    Is there an isotropic form of that metric which shows more explicitly there is no difference looking along x or y or z direction from the center. It must look something like

    [tex] ds^2 = - A^2(r,t) dt^2 + B^2(r,t) (dx^2 + dy^2 + dz^2 )[/tex]
    where [tex] r = \sqrt{x^2 + y^2 + z^2} [/tex]

    I know the above is spherically symmetric, the question is wether it's the most general form? Any references I should check?

    As an example the isotropic form of a general FRW metric is:

    [tex] ds^2 = - dt^2 + \frac{a(t)^2}{(1+kr^2/4)^2} (dx^2 + dy^2 + dz^2 )[/tex]
    Last edited: Apr 2, 2008
  2. jcsd
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