It has been shown recently that extreme Reissner-Nordström black holes perturbed by a minimally coupled, free, massless scalar field have permanent scalar hair. The hair, a conserved charge calculated at the black hole's event horizon, can be measured by a certain expression at future null infinity: The latter approaches the hair inversely in time. We generalize this newly discovered hair also for extreme Kerr black holes. We study the behavior of nearly extreme black hole hair and its measurement at future null infinity as a transient phenomenon. For nearly extreme black holes the measurement at future null infinity of the length of the newly grown hair decreases quadratically in time at intermediate times until its length becomes short and the rate at which the length shortens further slows down. Eventually, the nearly extreme black hole becomes bald again like nonextreme black holes.

• Received 7 June 2019

DOI:https://doi.org/10.1103/PhysRevResearch.1.033106

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society