General relativistic tidal heating for the M$\o$ller 58 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 this tidal heating must be independent of how one localizes gravitational energy and is unambiguously given by that expression. Favata calculated the tidal heating for a number of classical gravitational pseudotensors including that of M$\o$ller, and obtained the result that all of them produced the same (Newtonian) value. After a re-examination of the calculation using the M$\o$ller pseudotensor we find that indeed this pseudotensor gives the desired result under the condition that the mass $M$ is a constant, while Favata considered $M$ as being time dependent, which is illegitimate since it violates the harmonic gauge condition, which he used. Moreover, we carry on to consider this M$\o$ller pseudtensor even in a black hole situation, i.e., beyond Newtonian physics.