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Journal Article

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

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##### Fulltext (public)

1209.0213.pdf

(Preprint), 407KB

CQG_30_5_055011.pdf

(Any fulltext), 377KB

##### Supplementary Material (public)

There is no public supplementary material available

##### Citation

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.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0015-195D-5

##### Abstract

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.