University of Cambridge > Talks.cam > DAMTP Friday GR Seminar > Stability and Instability of Extreme Reissner-Nordstrom Black Hole Spacetimes for Linear Scalar Perturbations

Stability and Instability of Extreme Reissner-Nordstrom Black Hole Spacetimes for Linear Scalar Perturbations

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We consider solutions of the linear wave equation on extreme Reissner-Nordstrom. The wave equation on black hole backgrounds has been the object of intense study during the last decade. Decay results have been established for solutions to the linear wave equation on several subextreme black holes. However, the methods and techniques that have been developed break down in the case of extreme black holes, where the redshift effect degenerates. In this talk, I am going to derive pointwise decay of the solutions to the wave equation on extreme Reissner-Nordstrom and show that the transversal to the horizon derivatives do not decay. In fact, I will derive pointwise and energy blow-up estimates for the higher order transversal to the horizon derivatives. Several new analytical features of degenerate horizons will also be presented.

This talk is part of the DAMTP Friday GR Seminar series.

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