Black Holes Lessons from Multipole Ratios: A New Window into Black Holes

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Iosif Bena (Université Paris Saclay)

We compute gravitational mass and angular momentum multipole moments for four-dimensional black holes and fuzzball geometries thereof. For Kerr and for supersymmetric black holes many multipole moments vanish, but we show that an infinite number of ratios of vanishing multipoles are constant. We calculate these ratios for the first time, using two very different methods; the results agree spectacularly for certain black holes. Hence our work establishes that ratios of vanishing multipoles are intrinsic properties of four-dimensional black holes. For the Kerr black hole these ratios pose strong constraints on the parameterization of possible deviations from the Kerr geometry that should be tested by future gravitational wave interferometers.


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