Multipole moments do not uniquely characterize spacetimes beyond general relativity
arXiv:2511.22405
Abstract
Spacetimes in general relativity can be uniquely decomposed into a set of multipole moments. Given the usefulness of moments in the categorization of radiation patterns, tidal deformations, and other phenomena associated with compact objects, a number of studies have explored their construction in beyond-Einstein theories of gravity. It is shown here that uniqueness does not necessarily extend across theories: by comparing a few static and spherically-symmetric solutions in different theories, we find that two distinct objects can possess the same Geroch-Hansen moments. Moreover, two metrics can match and yet take different moments. Implications of this result are explored in the context of black-hole shadows and ``universal'' relations hinging on moment computations.
8 pages, 1 figure, 1 table. Accepted for publication in Phys. Rev. D