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arXiv · 2312.04352

Gravitational Multipoles in Five Dimensions

Jef Heynen·Daniel R. Mayerson
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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.

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Jef Heynen, Daniel R. Mayerson. 2023-12-07. Gravitational Multipoles in Five Dimensions. https://arxiv.org/abs/2312.04352

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