Abstract
There is considerable freedom in the definition of multipole moments of the energy-momentum tensor of an extended body in general relativity. By studying the corresponding Newtonian theory we obtain guidelines which enable us to choose the most suitable definitions in the relativistic theory. In this way we find two sets, the complete moments and the reduced moments, of which the latter are the most natural choice for studying the dynamics of extended bodies. Expressions as explicit integrals are give for both sets, and the multipole equations of motion of the body are given in a form exact to all orders. Proofs of the relativistic results will appear elsewhere.
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Dixon, W.G. The definition of multipole moments for extended bodies. Gen Relat Gravit 4, 199–209 (1973). https://doi.org/10.1007/BF02412488
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DOI: https://doi.org/10.1007/BF02412488