Contents/conteúdo

Mathematical Relativity Seminar   RSS

Planned sessions

21/10/2019, 11:00 — 12:00 — Room P3.10, Mathematics BuildingInstituto Superior Técnicohttp://tecnico.ulisboa.pt
Amol Sasane, London School of Economics

Decay of solutions to the Klein-Gordon equation on some expanding cosmological spacetimes

The decay of solutions to the Klein-Gordon equation is studied in two expanding cosmological spacetimes, namely the de Sitter universe in flat Friedmann-Lemaître-Robertson-Walker (FLRW) form, and the cosmological region of the Reissner-Nordström-de Sitter (RNdS) model. Using energy methods, for initial data with finite higher order energies, decay rates for the solution are obtained. Also, a previously established decay rate of the time derivative of the solution to the wave equation, in an expanding de Sitter universe in flat FLRW form, is improved, proving Rendall's conjecture. A similar improvement is also given for the wave equation in the cosmological region of the RNdS spacetime.

03/01/2020, 14:00 — 15:00 — Room P3.10, Mathematics BuildingInstituto Superior Técnicohttp://tecnico.ulisboa.pt
Rita Teixeira da Costa, University of Cambridge

Mode stability for the Teukolsky equation on extremal Kerr black hole spacetimes

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 show that the proof for the latter cannot be extended to 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.


Current organizers: José Natário, João Lopes Costa

CAMGSD FCT