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arXiv · 2412.19667

Multipole moments in stationary spacetimes

Jorn van Voorthuizen
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Abstract

Multipole moments in general relativity serve as a powerful tool for characterising the gravitational field. In this paper, we review the construction of the Geroch--Hansen multipole moments for stationary asymptotically flat vacuum spacetimes. A particular focus is placed on the well-definedness of these moments, which hinges on the uniqueness of the one-point conformal completion in Geroch's asymptotic flatness definition. Based on Geroch's approach, we formulate and prove a revised uniqueness result, thereby filling in some gaps in the original approach. Uniqueness holds up to certain conformal transformations, and we discuss how the multipole moments behave under such transformations.

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Jorn van Voorthuizen. 2024-12-27. Multipole moments in stationary spacetimes. https://doi.org/10.1063/5.0256660

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