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Applications of the Gaussian Beam approximation to black hole spacetimes

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If you have a question about this talk, please contact Dr Joan Camps .

Motivated by the black hole stability problem, various people have studied the wave equation on black hole spacetimes. In particular, it is of interest to prove local energy decay (LED) for waves. However, due to the presence of trapping in black hole spacetimes, there is a well-known heuristic obstruction to LED , namely the existence of highly oscillatory solutions to the wave equation whose energies stay localised for arbitrarily long, but finite time. This only allows for a “weaker” form of LED to hold. In this talk, using the Gaussian Beam approximation, we will make these heuristics rigorous. In particular, we present a characterisation of the energy of a Gaussian Beam, which is a crucial ingredient for the above undertaking.

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

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