Show that conditions (i), (ii), and (iii) preceding Eq. (27.48) guarantee that the multipolar expansion of the

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Show that conditions (i), (ii), and (iii) preceding Eq. (27.48) guarantee that the multipolar expansion of the gravitational-wave fields will have the form (27.48).


Conditions

The wave fields h+ and h× in the source’s local wave zone must 

(i) Be dimensionless, 

(ii) Die out as 1/r, 

(iii) Be expressed as a sum over derivatives of the multipole moments. These considerations guarantee that the waves will have the following form:

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