Gravitational Multipoles in Five Dimensions

Abstract

We define gravitational mass and current multipoles for five-dimensional, stationary, and asymptotically flat vacuum metrics. We do this by generalizing Thorne's asymptotically Cartesian and mass-centered (ACMC) coordinate formalism to five dimensions, and prove that the multipoles defined in this way are unambiguously well-defined. Further, these two towers of multipole tensors, in the case of biaxial symmetry, reduce to a tower of mass multipoles $M_\ell$, and two separate towers of current or angular momentum multipoles $S^{(1)}_\ell, S^{(2)}_\ell$. We apply our formalism to a few examples, in particular Myers-Perry black holes, black rings, and smooth multicentered geometries.