Surveys in Differential Geometry
Volume 20 (2015)
Decay of linear waves on black hole space-times
Pages: 157 – 182
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