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I Factor of 1/2 in gravitational potential energy

  1. Jul 28, 2016 #1
    I am currently reading Gravitational Curvature by Theodore Frankel. In the derivation of Einstein's equations in chapter 3, he states that the gravitational potential energy of a blob of fluid is


    where the integral is a volume integral, p0 is the rest energy density and √gvdx is the volume form.

    From what I understand p0√gvdx is an infinitesimal bit of mass, so why wouldn't the potential energy just be U times that bit of mass? Why ½ that?
  2. jcsd
  3. Jul 28, 2016 #2


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    Without that factor, you double-count the gravitational potential. This is easier to understand with discrete masses: You would sum over the potential of mass A due to B (using GMm/r) and the potential of mass B due to A (using GMm/r again), but the actual potential energy for both together is just one time GMm/r.
  4. Jul 28, 2016 #3
    That makes much more sense. Thank you
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