ICTS

In this talk I will discuss leading order late time decay tails of massless scalar perturbations outside an extreme Reissner-Nordstr\"om black hole. We analyse the problem in the frequency domain. We first consider initial perturbations with generic regular behaviour across the horizon on characteristic surfaces. For this set-up, we reproduce some of the previous results of Sela using Fourier methods. Next, we consider related initial data  on t=const hypersurfaces, and present decay results at timelike infinity,  near future null infinity, and near the future horizon. Along the way, using a special inversion symmetry of the extreme Reissner-Nordstr\"om spacetime, we relate the higher multipole Aretakis and Newman-Penrose constants for a massless scalar in this background.

Link: https://arxiv.org/abs/1805.10655