Mathematical Relativity Seminar   RSS

Planned sessions

06/12/2019, 14:30 — 15:30 — Room P4.35, Mathematics Building Instituto Superior Técnico
Ernesto Nungesser, ICMAT – Institute of Mathematical Sciences

03/01/2020, 14:00 — 15:00 — Room P3.10, Mathematics Building Instituto Superior Técnico
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.

16/01/2020, 14:30 — 15:30 — Seminar room (2.8.3), Physics Building Instituto Superior Técnico
Miguel Duarte, Instituto Superior Técnico

Conformally flat slices of asymptotically flat spacetimes

For mathematical convenience initial data sets in numerical relativity are often taken to be conformally flat. Employing the dual-foliation formalism, we investigate the physical consequences of this assumption. Working within a large class of asymptotically flat spacetimes we show that the ADM linear momentum is governed by the leading Lorentz part of a boost even in the presence of supertranslation-like terms. Following up, we find that in spacetimes that are asymptotically flat, and admit spatial slices with vanishing linear momentum that are sufficiently close to conformal flatness, any boosted slice can not be conformally flat. Consequently there are no conformally flat boosted slices of the Schwarzschild spacetime. This confirms the previously anticipated explanation for the presence of junk-radiation in Brandt-Bruegmann puncture data.

This seminar is joint with CENTRA, and will take place on the Physics Department (seminar room, 2nd floor).

Current organizers: José Natário, João Lopes Costa