What is the shape of a spinning black hole? | Colóquio do DFMA

Abstract: In his monographs Ellipsoidal Figures of Equilibrium and The Mathematical Theory of Black Holes, Subrahmanyan Chandrasekhar developed a comprehensive treatment of self-gravitating fluid configurations and black hole spacetimes in general relativity, respectively. Bringing these two lines of thought into dialogue raises a natural but subtle question: what is the "shape" of a spinning black hole, and in what sense can such a notion even be defined in general relativity? In this talk, we introduce three complementary notions of shape, based on asymptotic (field multipoles), quasi-local (horizon geometry), and dynamical (tidal response) characterizations of Kerr black holes. Finally, we discuss how these notions are (partially) encoded into gravitational-wave signals, in particular from extreme mass-ratio inspirals relevant for LISA, providing a route toward precision tests of the no-hair theorem and a form of black hole tomography.

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