For scalar perturbations of an extreme Reissner-Nordström black hole we show numerically that the Ori prefactor equals the Aretakis conserved charge. For a family of scalar or gravitational perturbations of an extreme Kerr black hole, whose members vary only in the radial location of the center of the initial packet, we demonstrate a linear relation of a generalized Ori prefactor—a certain expression obtained from the late-time expansion or the perturbation field at finite distances—and the Aretakis conserved charge. We infer that it can be established that there is an Aretakis conserved charge for scalar or gravitational perturbations of extreme Kerr black holes. This conclusion, in addition to the calculation of the Aretakis charge, can be made from measurements at a finite distance: Extreme Kerr black holes have gravitational hair that can be measured at finite distances and violates the uniqueness theorems. This gravitational hair can in principle be detected by gravitational-wave detectors.

• Received 13 May 2020
• Accepted 15 December 2020

DOI:https://doi.org/10.1103/PhysRevD.103.L021502