# Rita Teixeira da Costa: Mode stability for the Teukolsky equation on extremal Kerr black hole spacetimes

**Time: **
Tue 2019-12-10 11.00 - 12.00

**Location: **
Institut Mittag-Leffler, Seminar Hall Kuskvillan

**Lecturer: **
Rita Teixeira da Costa, University of Cambridge

### Abstract

We prove that there are no exponentially growing modes nor modes on the real axis for the Teukolsky equation on extremal Kerr black hole spacetimes. While the result was previously known for subextremal spacetimes, we argue that the proof for the latter does not hold in the extremal case as the nature of the event horizon changes radically in the extremal limit.

Finally, we explain how mode stability could serve as a preliminary step towards understanding boundedness, scattering and decay properties of general solutions to the Teukolsky equation on extremal Kerr black holes.