Communications in Mathematical Physics

, Volume 264, Issue 2, pp 465-503

First online:

Decay of Solutions of the Wave Equation in the Kerr Geometry

  • F. FinsterAffiliated withNWF I – Mathematik, Universität Regensburg Email author 
  • , N. KamranAffiliated withDepartment of Math. and Statistics, McGill University
  • , J. SmollerAffiliated withMathematics Department, The University of Michigan
  • , S.-T. YauAffiliated withMathematics Department, Harvard University

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


We consider the Cauchy problem for the massless scalar wave equation in the Kerr geometry for smooth initial data compactly supported outside the event horizon. We prove that the solutions decay in time in L 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 ω on the real line. This integral representation involves solutions of the radial and angular ODEs which arise in the separation of variables.