
or its much more useful and attractive (real) form
Remark 12. The Bondi mass, , and the original mass of the Reissner–Nordström (Schwarzschild) unperturbed metric, , i.e., the harmonic of , differ by a quadratic term in the shear, the part of . This suggests that the observed mass of an object is partially determined by its timedependent quadrupole moment.
Upon extracting the harmonic portion of Eq. (6.51) as well as inserting our various physical identifications for the objects involved, we obtain the Bondi mass loss theorem:
This mass/energy loss equation contains the classical energy loss due to electric and magnetic dipole radiation and electric and magnetic quadrupole () radiation. (Note that agreement with the physical quadrupole radiation is recovered after making the aforementioned rescaling .) The gravitational energy loss is the conventional quadrupole loss by the identification (6.36) of with the gravitational quadrupole moment .The momentum loss equation, from the part of Eq. (6.51), is then identified with the recoil force due to momentum radiation:

where
Finally, we can substitute in the from Eq. (6.49) to obtain Newton’s second law of motion: with
There are several things to observe and comment on concerning Eqs. (6.54) and (6.55):
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Living Rev. Relativity 15, (2012), 1
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