Corrections to the Aretakis type behaviour of the metric due to an infalling particle

Abstract

We consider an extremal Reissner-Nordström black hole perturbed by a neutral massive point particle, which falls in radially. We study the linear metric perturbation in the vicinity of the black hole and find that the $l=0$ and $l=1$ spherical modes of the metric oscillate rather than decay.

7 pages, title is changed, clarifications are added