Scalar and gravitational transient hair for near-extremal black holes

We study the existence and nature of Aretakis charge 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 and Kerr. 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 nonextremal 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.