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Gaussian beams on Lorentzian manifolds

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If you have a question about this talk, please contact Prof. Neshan Wickramasekera .

In this talk we first briefly review how one can use the Gaussian beam approximation for constructing solutions to the wave equation on general globally hyperbolic Lorentzian manifolds whose energy is localised along a given null geodesic for a finite, but arbitrarily long time. In the very special case that the Lorentzian manifold admits a timelike Killing vector field, one can easily show that the energy of waves is a conserved quantity. For general Lorentzian manifolds however, the energy of waves varies in time. In this talk we present a geometric characterisation of the temporal behaviour of the energy of the above mentioned Gaussian beams. We conclude the talk with applications to the study of the wave equation on black hole spacetimes which arise in general relativity.

This talk is part of the Geometric Analysis & Partial Differential Equations seminar series.

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