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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Maths HEP Lunchtime Seminars: Boundedness and decay for the wave equation on Kerr and other axisymmetric stationary black hole backgrounds

Presented by Mihalis Dafermos, Cambridge University

20 March 2009 13:00 in CLC407

Understanding the behaviour of linear waves on black hole backgrounds is a
central problem in general relativity, intimately connected with the
nonlinear stability of the black hole spacetimes themselves as solutions
to the Einstein equations--a major open question in the subject.
Nonetheless, it is only very recently that even the most basic boundedness
and quantitative decay properties of linear waves have been proven in a
suitably general class of black hole exterior spacetimes. This talk will
review our current mathematical understanding of waves on black hole
backgrounds, beginning with the classical boundedness theorem of Kay and
Wald on exactly Schwarzschild exteriors and ending with very recent
boundedness and decay theorems (proven in collaboration with Igor
Rodnianski) on a wider class of spacetimes. This class of spacetimes
includes in particular slowly rotating Kerr spacetimes, but in the case of
the boundedness theorem is in fact much larger, encompassing general
axisymmetric stationary spacetimes whose geometry is sufficiently close to
Schwarzschild and whose Killing fields span the null generator of the

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