General relativistic tidal heating for the Moller pseudotensor

In his study of tidal stabilization of fully relativistic neutron stars Thorne showed that the fully relativistic expression for tidal heating is the same as in non-relativistic Newtonian theory. Furthermore, Thorne also noted that the tidal heating must be independent of how one localizes gravitational energy and is unambiguously given by that expression. Purdue and Favata calculated the tidal heating for a number of classical gravitational pseudotensors including that of Moller, and obtained the result that all of them produced the same (Newtonian) value. However, in a re-examination of the calculation using the Moller pseudotensor we find that there is no tidal heating. This leads us to the conclusion that Thorne's assertion needs a minor modification: the relativistic tidal heating is pseudotensor independent only if the pseudotensor is derived from a Freud type superpotential.