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Consider a spherical symmetric mass distribution in space, located around the origin of a coordinate system. One can forumlate a stress-energy-tensor $T^{\mu,\nu}$ for this situation. Solving the Einstein-field-equations for a reference frame, in which that mass distribution is not moving one obtains the Schwarzschild-metric $g_{\mu,\nu}$. One can now try ...


m includes all kinds of energies for the mass at rest, including the thermal energy, and those from the other degrees of freedom, such as the ones internal to the nucleus, as AnnaV mentioned. So you only have to compute mc^2, the HTM term is redundant.

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