Extremal Black Hole Weather
Claudio Iuliano, Stefan Hollands, Stephen R. Green, Peter Zimmerman

TL;DR
This paper investigates the non-linear evolution of gravitational perturbations near extremal Kerr black holes, revealing a stable mode distribution that resembles weather phenomena and is driven by weakly non-linear effects.
Contribution
It introduces a non-linear dynamical system for quasinormal mode amplitudes and finds a stable, exponentially suppressed mode distribution as an endpoint of evolution.
Findings
Existence of a time-independent equilibrium solution for mode amplitudes.
Mode amplitudes decay exponentially with angular momentum number ^{-rac{ ext{l}}{2}}.
Evolution approaches a mode distribution akin to atmospheric weather patterns.
Abstract
We consider weakly non-linear gravitational perturbations of a near-extremal Kerr black hole governed by the second order vacuum Einstein equation. Using the GHZ formalism [Green et al., Class. Quant. Grav. 7(7):075001, 2020], these are parameterized by a Hertz potential. We make an ansatz for the Hertz potential as a series of zero-damped quasinormal modes with time-dependent amplitudes, and derive a non-linear dynamical system for them. We find that our dynamical system has a time-independent solution within the near horizon scaling limit. This equilibrium solution is supported on axisymmetric modes, with amplitudes scaling as for large polar angular momentum mode number , where is a cumulative amplitude of the low modes. We interpret our result as evidence that the dynamical evolution will approach,…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsRelativity and Gravitational Theory · Astrophysical Phenomena and Observations · Experimental and Theoretical Physics Studies
