Re: Double counting gravitational potential energy

Cracked it!

After being very helpfully reminded on the Physics Forums to reread
MTW box 23.1 more carefully, I now understand that the source of the
paradox is entirely in the internal energy of the pressure term need
to maintain equilibrium. In the case where the central object is
stable, this pressure term gives rise to exactly the same energy as
the external potential energy, balancing out the double decrease in
the rest mass.

What really confused me in this case is the fact that I had been
taught long ago that the nominal first order "rest mass" of the
central object is m(1-Gm/rc^2), without mentioning that this EXCLUDES
the internal energy. The overall effective rest mass INCLUDING the
internal energy is however m(1-Gm/2rc^2), matching the potential
energy loss in forming the body.

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