Gravity seminar - Georgios Moschidis Seminar

In this talk, I will present two results illustrating the role of superradiance as a mechanism of instability for the scalar wave equation \square_g \psi=0. In the first part of the talk, I will show that, on the rotating subextremal Kerr exterior spacetime, superradiance is sufficiently strong to lead to mode instability for equation \square_g \psi - V \psi=0 for a stationary, positive and compact in space potential V, despite the fact that solutions to the free scalar wave equation \square_g \psi=0 decay polynomially in time (as was established by Dafermos-Rodnianski-Shlapentokh-Rothman). This can be thought of as "designer superradiance instabilities", extending the instability results of Shlapentokh-Rothman for the Klein-Gordon equation \square_g \psi-\mu^2 \psi=0. In the second part of the talk, I will consider the general case of stationary and asymptotically flat spacetimes possessing an ergoregion and no event horizon. For such spacetimes, I will provide a rigorous proof of Friedman's instability for scalar waves. I will also present some applications in the case of the acoustic wave equation on a supersonic fluid flow.