A remark about wave equations on the extreme Reissner-Nordström black hole 
exterior

Bizon, Piotr; Friedrich, Helmut

doi:10.1088/0264-9381/30/6/065001

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A remark about wave equations on the extreme Reissner-Nordström black hole exterior

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Friedrich, Helmut
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1212.0729
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Citation

Bizon, P., & Friedrich, H. (2013). A remark about wave equations on the extreme Reissner-Nordström black hole exterior. Classical and quantum gravity, 30(6): 065001. doi:10.1088/0264-9381/30/6/065001.

Cite as: https://hdl.handle.net/11858/00-001M-0000-000E-7C80-3

Abstract

We consider a massless scalar field propagating on the exterior of the extreme Reissner-Nordstr\"om black hole. Using a discrete conformal symmetry of this spacetime, we draw a one-to-one relationship between the behavior of the field near the future horizon and near future null infinity. In particular, we show that the polynomial growth of the second and higher transversal derivatives along the horizon, recently found by Aretakis, reflects well known facts about the retarded time asymptotics at null infinity.