Bäckdahl, Thomas: Methods for proving decay of fields on black hole spacetimes

It is expected that perturbations of stationary black holes described by
the Kerr spacetime, will decay due to emission of gravitational waves.
In other words; non-linear stability of the Kerr black hole is expected.
However, this is difficult to mathematically prove, due to the structure
and non-linearlities of Einstein's field equations. Over the last
decades techniques have been developed to prove decay of linear and
non-linear wave equations, which are important model problems. In this
talk, I will present one of these methods, and how it can possibly be
extended to prove decay of Maxwell fields on black hole spacetimes. The
Maxwell field incorporates more of the features of the gravitational
field, and is therefore a better model problem. The methods are built
from the geometry of the problem, in particular the (hidden) symmetries
of the spacetime.