  When a self-gravitating body (e.g., a neutron star or black hole) interacts
with an external tidal field (e.g., that of a binary companion), the
interaction can do work on the body, changing its mass-energy. The details of
this "tidal heating" are analyzed using the Landau-Lifshitz pseudotensor and
the local asymptotic rest frame of the body. It is shown that the work done on
the body is gauge-invariant, while the body-tidal-field interaction energy
contained within the body's local asymptotic rest frame is gauge dependent.
This is analogous to Newtonian theory, where the interaction energy is shown to
depend on how one localizes gravitational energy, but the work done on the body
is independent of that localization.
