Scaling and Universality in Extremal Black Hole Perturbations

TL;DR

This paper demonstrates that extremal black holes exhibit universal perturbation behaviors governed by near-horizon conformal symmetry, revealing scale-invariance, specific decay rates, and instabilities across various fields, explained via holography.

Contribution

It establishes universal features of perturbations in extremal black holes derived from near-horizon conformal symmetry, including decay rates and instabilities, applicable to multiple field types.

Findings

Decay off the horizon is twice as fast as on the horizon.

Universal decay rates of 1/t and 1/√v are identified.

High-order derivatives grow on the horizon indicating Aretakis instability.

Abstract

We show that the emergent near-horizon conformal symmetry of extremal black holes gives rise to universal behavior in perturbing fields, both near and far from the black hole horizon. The scale-invariance of the near-horizon region entails power law time-dependence with three universal features: (1) the decay off the horizon is always precisely twice as fast as the decay on the horizon; (2) the special rates of $1/t$ off the horizon and $1/\sqrt{v}$ on the horizon commonly occur; and (3) sufficiently high-order transverse derivatives grow on the horizon (Aretakis instability). The results are simply understood in terms of near-horizon ($\mathrm{AdS}_2$) holography. We first show how the general features follow from symmetry alone and then go on to present the detailed universal behavior of scalar, electromagnetic, and gravitational perturbations of $d$-dimensional electrovacuum black holes.