# Stability and instability results for scalar waves on general asymptotically flat spacetimes

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Georgios Moschidis , Princeton University
Fine Hall 110

In the first part of this talk, we will prove a logarithmic decay result for solutions to the scalar wave equation $\square_{g}\psi=0$ on general asymptotically flat spacetimes $(\mathcal{M},g)$, possibly bounded by an event horizon with positive surface gravity and having a small ergosphere, provided a uniform energy boundedness estimate holds on $(\mathcal{M},g)$. This result generalises of a result of Burq for the wave equation on the complement of an arbitrary compact obstacle in flat space. The methods developed for the proof of this result will then be applied, in the second part of the talk, in obtaining a rigorous proof of Friedman's ergosphere instability for scalar waves.