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

Question:

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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Modern Classical Physics Optics Fluids Plasmas Elasticity Relativity And Statistical Physics

ISBN: 9780691159027

1st Edition

Authors: Kip S. Thorne, Roger D. Blandford

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Question Posted: Jul 01, 2023 02:50 AM

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

Question:

h+~hx მ2Z,/მr2 მ3x3/მr3 r r & & ... & მ2S2/მr2 მ3S3/მ13 & r r & (27.48)

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Modern Classical Physics Optics Fluids Plasmas Elasticity Relativity And Statistical Physics

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