It is well known that, when an external general relativistic (electric-type)
tidal field E(t) interacts with the evolving quadrupole moment I(t) of an
isolated body, the tidal field does work on the body (``tidal work'') -- i.e.,
it transfers energy to the body -- at a rate given by the same formula as in
Newtonian theory: dW/dt = -1/2 E dI/dt. Thorne has posed the following
question: In view of the fact that the gravitational interaction energy between
the tidal field and the body is ambiguous by an amount of order E(t)I(t), is
the tidal work also ambiguous by this amount, and therefore is the formula
dW/dt = -1/2 E dI/dt only valid unambiguously when integrated over timescales
long compared to that for I(t) to change substantially? This paper completes a
demonstration that the answer is no; dW/dt is not ambiguous in this way. More
specifically, this paper shows that dW/dt is unambiguously given by -1/2 E
dI/dt independently of one's choice of how to localize gravitational energy in
general relativity. This is proved by explicitly computing dW/dt using various
gravitational stress-energy pseudotensors (Einstein, Landau-Lifshitz, Moller)
as well as Bergmann's conserved quantities which generalize many of the
pseudotensors to include an arbitrary function of position. A discussion is
also given of the problem of formulating conservation laws in general
relativity and the role played by the various pseudotensors.Comment: 15 pages, no figures, revtex. Submitted to Phys. Rev.
