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Metric Solves Grav. Gauss' Law (1/2)

  1. Start with Gen. Gauss' law:

  2. Assume no electric charges or electromagnetic fields. Assume static:

  3. Write out covariant derivative:

  4. Want everything to depend on the metric like in general relativity. Choose a potential such that :

Note: the divergence of the Christoffel symbol, cool!