Surveys in Differential Geometry

Volume 20 (2015)

Decay of linear waves on black hole space-times

Pages: 157 – 182

DOI: https://dx.doi.org/10.4310/SDG.2015.v20.n1.a7

Author

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

Abstract

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.

Keywords

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

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Published 7 July 2015