Surveys in Differential Geometry

Volume 20 (2015)

Decay of linear waves on black hole space-times

Pages: 157 – 182



Daniel Tataru (Department of Mathematics, University of California at Berkeley)


The aim of these notes is to describe recent and ongoing work of the author and collaborators on decay estimates for linear waves on black hole space times. For comparison purposes, our discussion will also include nontrapping asymptotically flat space-times. We will consider the scalar wave equation and perturbations thereof, as well as the corresponding Maxwell system.


Kerr spacetime, black hole stability, decay of linear waves, waves, Maxwell system, energy estimates, Strichartz estimates, Morawetz estimates

2010 Mathematics Subject Classification

35L05, 35Q61, 35Q76, 83C57

Published 7 July 2015