Scalar and Gravitational Transient "Hair" for Near-Extremal Black Holes

TL;DR

This paper investigates the existence of transient scalar and gravitational 'hair' around near-extremal black holes, showing that Aretakis charges decay slowly near extremality, potentially allowing observational detection.

Contribution

It numerically analyzes Aretakis charges in near-extremal black holes, revealing their slow decay and transient nature, which was not previously characterized.

Findings

Aretakis charges are not strictly conserved in near-extremal cases.

Decay of charges can be arbitrarily slow near extremality.

Transient hair may be observable at finite distances from the horizon.

Abstract

We study the existence and nature of Aretakis "hair" and its potentially observable imprint at a finite distance from the horizon (Ori-coefficient) in near-extremal black hole backgrounds. Specifically, we consider the time evolution of horizon penetrating scalar and gravitational perturbations with compact support on near-extremal Reissner-Nordstrom (NERN) and Kerr (NEK). We do this by numerically solving the Teukolsky equation and determining the Aretakis charge values on the horizon and at a finite distance from the black hole. We demonstrate that these values are no longer strictly conserved in the non-extremal case; however, their decay rate can be arbitrarily slow as the black hole approaches extremality allowing for the possibility of their observation as a transient hair.