Mimicking Kerr's multipole moments
B\'eatrice Bonga, Huan Yang
TL;DR
This paper constructs Newtonian models with multipole moments identical to Kerr black holes and discusses incorporating post-Newtonian corrections, challenging the uniqueness of Kerr's multipole characterization.
Contribution
It introduces Newtonian objects matching Kerr's multipole moments and details how to include post-Newtonian corrections without altering these moments.
Findings
Newtonian models with Kerr multipole moments constructed
Post-Newtonian corrections can be added while preserving moments
Challenges the uniqueness of Kerr's multipole characterization
Abstract
Multipole moments carry a lot of information about the gravitational field. Nonetheless, knowing all the multipole moments of an object does not determine conclusively the nature of the object itself. In particular, the multipole moments of the Kerr spacetime are not unique. Here we construct several physically motivated Newtonian objects with multipole moments identical to those of Kerr. Moreover, we also provide a description of how to include post-Newtonian corrections to these objects without changing their multipole moments.
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