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Weak field relativity - with future applications to the moving mass discussion

  1. Sep 27, 2005 #1

    pervect

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    Pete, the latex isn't working in the private messages, so I posted this:

    Do you agree with the following mass of statements (sorry for the length), I'll number them for reference

    #1)
    In the weak field, g_uv = n_uv + h_uv, h_uv <<1, and we raise and lower indices with n_uv, not h_uv.

    #2)
    In the weak field the Christoffel symbols are

    [edit] factor of 1/2 added [/end edit]

    [tex]
    \Gamma^c{}_{ab} = \frac{1}{2} n^{cd} (\partial_a\, g_{bd} + \partial_b\, g_{ad} - \partial_d \, g_{ab})
    [/tex]

    #3)

    In the weak field, the Riemann is

    [tex]R^a{}_{bcd} = \partial_c \, \Gamma^a{}_{bd} - \partial_d \,\Gamma^a{}_{bc} [/tex]

    ps - glad you're out of surgery & hope you're doing as well as you sound.
     
    Last edited: Sep 27, 2005
  2. jcsd
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