MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Decay of Solutions of the Wave Equation in the Kerr Geometry

Felix Finster, Niky Kamran, Joel Smoller and Shing-Tung Yau


We consider the Cauchy problem for the scalar wave equation in the Kerr geometry for smooth initial data supported outside the event horizon. We prove that the solutions decay in time in $L^{\infty}_{loc}$. The proof is based on a representation of the solution as an infinite sum over the angular momentum modes, each of which is an integral of the energy variable on the real line. This integral representation involves solutions of the radial and angular ODEs which arise in the separation of variables.


Related publications

2006 Repository Open Access
Felix Finster, Niky Kamran, Joel Smoller and Shing-Tung Yau

Decay of solutions of the wave equation in the Kerr geometry

In: Communications in mathematical physics, 264 (2006) 2, pp. 465-503