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#### The wave equation on the extreme Reissner-Nordström black hole

##### MPG-Autoren

Dain,  Sergio
AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

##### Externe Ressourcen
Es sind keine Externen Ressourcen verfügbar
##### Volltexte (frei zugänglich)

1209.0213.pdf
(Preprint), 407KB

CQG_30_5_055011.pdf
(beliebiger Volltext), 377KB

##### Ergänzendes Material (frei zugänglich)
Es sind keine frei zugänglichen Ergänzenden Materialien verfügbar
##### Zitation

Dain, S., & Dotti, G. (2013). The wave equation on the extreme Reissner-Nordström black hole. Classical and quantum gravity, 30(5): 055011. doi:10.1088/0264-9381/30/5/055011.

We study the scalar wave equation on the open exterior region of an extreme Reissner-Nordström black hole and prove that, given compactly supported data on a Cauchy surface orthogonal to the timelike Killing vector field, the solution, together with its $(t,s,\theta,\phi)$ derivatives of arbitrary order, $s$ a tortoise radial coordinate, is bounded by a constant that depends only on the initial data. Our technique does not allow to study transverse derivatives at the horizon, which is outside the coordinate patch that we use. However, using previous results that show that second and higher transverse derivatives at the horizon of a generic solution grow unbounded along horizon generators, we show that any such a divergence, if present, would be milder for solutions with compact initial data.