Universal quasinormal modes of large D black holes

TL;DR

The paper addresses how the quasinormal-mode spectrum of large-$D$ black holes simplifies in the $D\to\infty$ limit. It derives a universal set of modes whose complex frequencies depend only on the horizon radius, with damping shrinking as $D^{-2/3}$ and a spectrum described by Airy-function zeros, indicating quasi-normal, long-lived excitations. Using a tensor perturbation reduction to a scalar-like equation and a peaked near-horizon potential that becomes triangular at large $D$, the authors show that the universal spectrum is largely independent of charges, dilatons, or other black-hole parameters. This universality, applicable to a wide class of static black holes and perturbations, suggests a simplified, horizon-focused description in the large-$D$ regime and points toward deeper microscopic interpretations.

Abstract

We show that in the limit where the number of spacetime dimensions D grows to infinity a very large class of black holes (including non-extremal, static, asymptotically flat ones, with any number of gauge-field charges, possibly coupled to dilatons) possess a universal set of quasinormal modes whose complex frequencies depend only on the horizon radius and no other black hole parameters. The damping ratio of these modes vanishes like $D^{-2/3}$, so they are almost normal modes, or 'quasi-particle' excitations of the black hole. The structure responsible for the existence of these modes at large D is also present very generally in other black holes.

Figures (1)

• Figure 1: Effective potential $V(r_*)$ at large $D$. When $D\to\infty$, $V$ is given by \ref{['niftyV']} and the maximum becomes a sharp peak. Quasinormal modes correspond to bound states in the inverted potential $-V$ (inset). The lowest ones are the Airy-function bound states of a triangular well.