2024/12/27 by Jorn van Voorthuizen, van Voorthuizen, Jorn
Physics and Astronomy · #Cosmology and Gravitation Theories #Pulsars and Gravitational Waves Research #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.2412.19667
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.