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Numerical Evidence for Non-Axisymmetric Gravitational "Hair" for Extremal Kerr Black Hole Spacetimes with Hyperboloidal Foliations
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Various generalizations of the scalar, axisymmetric "horizon hair" for extremal black holes have recently appeared in the literature. In this paper, we propose an expression for a non-axisymmetric gravitational "charge" and its potentially observable imprint at a finite distance from the horizon (Ori-coefficient) in extremal Kerr black hole backgrounds. Using a hyperboloidal foliation, we offer strong and robust numerical evidence for the potential existence of this horizon hair and its properties. Specifically, we consider the time evolution of horizon penetrating, quadrupolar and (subdominant) octupolar gravitational perturbations with compact support on extremal Kerr (EK) spacetime. We do this by numerically solving the Teukolsky equation and determining the conserved charge values on the horizon and at a finite distance from the black hole.
Forward citations
Cited by 2 Pith papers
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A Nonlinear Endpoint of Charged Horizon Instabilities
Charged scalar collapse can form dynamical extremal black holes whose horizons show divergent energy density and constant charge hair, with universal near-threshold scaling.
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Topical Collection-Hyperboloidal Foliations in the Era of Gravitational-Wave Astronomy: From Mathematical Relativity to Astrophysics
An editorial overview of a topical collection showing that hyperboloidal foliation methods have matured from linear perturbations toward nonlinear evolutions.
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