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Why R-1/2gR

  1. Feb 7, 2008 #1
    Why did Einstein chose R_ab - 1/2 g_ab R = k T_ab the Right side is basically saying the mass/energy causes the curvature and must be a conserved quantity, but why is the curvature expressed like it is on the LHS i know it is conserved through differentiation but why that and not any other variant of Riemann curvature?
  2. jcsd
  3. Feb 7, 2008 #2


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    The short answer is that this is the only second rank tensor that gives us an automatic concept of the conservation and energy.

    This happens because [itex]T_{uv} = 8 \pi G_{uv}[/itex], so that [itex]\nabla^u T_{uv}[/itex] is equal to zero, since [itex]\nabla^u G_{uv}[/itex]=0.

    A longer answer involves many subtle points, unfortunately.
  4. Feb 7, 2008 #3
    found it in MTW gravitation thank you thou
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