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On Late Time Tails in an Extreme Reissner-Nordström Black Hole: Frequency Domain Analysis

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Virmani,  Amitabh
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Bhattacharjee, S., Chakrabarty, B., Chow, D. D. K., Paul, P., & Virmani, A. (2018). On Late Time Tails in an Extreme Reissner-Nordström Black Hole: Frequency Domain Analysis. Classical and quantum gravity, 35(20 ): 205002. doi:10.1088/1361-6382/aade59.

Cite as: http://hdl.handle.net/21.11116/0000-0001-6940-1
Abstract
In this brief note, we revisit the study of the leading order late time decay tails of massless scalar perturbations outside an extreme Reissner-Nordstr\"om black hole. Previous authors have analysed this problem in the time domain; 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 [arXiv:1510.06169] using Fourier methods. Next, we consider related initial data on $t=\mbox{const}$ hypersurfaces, and present decay results at timelike infinity, near future null infinity, and near the future horizon. Along the way, using the $r_* \to -r_*$ 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.