Oberseminar Angewandte Mathematik

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jrahenbr

Nicolas Besset (Université Paris-Saclay): Parametrix construction and Fredholm theory for totally characteristic wave type operators. Oberseminar Topics in General Relativity

Tuesday, 28.06.2022 12:00 im Raum SRZ204

Mathematik und Informatik

Totally characteristic wave type operators naturally appear in cosmological black hole type spacetimes in General Relativity. We propose a parametrix construction for such operators using Mellin type quantization. We then deduce the index 0 Fredholm property which allows us to define resonances of these operators as the zeros of a Fredholm determinant. If time allows it, we will discuss how to use this method to numerically approximate resonances with control of the error.



Angelegt am Monday, 20.06.2022 11:25 von jrahenbr
Geändert am Monday, 20.06.2022 11:25 von jrahenbr
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Oberseminar Angewandte Mathematik
Bridging the Gaps Oberseminar Analysis'
Veranstaltungen am Mathematischen Institut
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jrahenbr

Dr. Christoph Kehle (ETH Zürich): Strong Cosmic Censorship for ? < 0. Oberseminar Topics in General Relativity

Tuesday, 21.06.2022 12:00 im Raum SRZ204

Mathematik und Informatik

The statement that general relativity is deterministic finds its mathematical formulation in the celebrated `Strong Cosmic Censorship Conjecture' due to Roger Penrose. I will present my results on the linear analog of this conjecture in the case of negative cosmological constant. It turns out that this is intimately tied to Diophantine properties of a suitable ratio of mass and angular momentum of the black hole due to the presence of slowly decaying quasinormal modes on the black hole exterior. If time permits, I will further discuss a related result (joint with M. Van de Moortel) on Strong Cosmic Censorship for spherical symmetry dynamical black holes in the presence of slow decay.



Angelegt am Monday, 20.06.2022 10:00 von jrahenbr
Geändert am Monday, 20.06.2022 10:00 von jrahenbr
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Oberseminar Angewandte Mathematik
Bridging the Gaps Oberseminar Analysis'
Veranstaltungen am Mathematischen Institut
|
jrahenbr

Christopher Straub (Universität Bayreuth): Linearly Stable Shells of Collisionless Matter Surrounding a Schwarzschild Black Hole. Oberseminar Topics in General Relativity

Tuesday, 05.07.2022 12:00 im Raum SRZ204

Mathematik und Informatik

The asymptotically flat Einstein-Vlasov system is used to describe the evolution of an isolated globular cluster or galaxy in a relativistic setting. We consider this system in Schwarzschild coordinates with a fixed central black hole as well as without singularity. After constructing compactly supported equilibria in these cases, we discuss their stability properties. We derive a sharp criterion for linear stability by developing a Birman-Schwinger type principle originating from quantum mechanics. We then conclude by discussing applications of our criterion, including the linear stability of "small" Vlasov matter shells surrounding a black hole. The talk is based on joint work with Sebastian Günther and Gerhard Rein.



Angelegt am Thursday, 23.06.2022 10:27 von jrahenbr
Geändert am Thursday, 23.06.2022 10:27 von jrahenbr
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Oberseminar Angewandte Mathematik
Bridging the Gaps Oberseminar Analysis'
Veranstaltungen am Mathematischen Institut