Abstracts
Abhay Ashtekar
The Many Faces of the Initial Value Formulation: A tribute to Prof. Yvonne Choquet
Mme Choquet has been an inspiring scientist to all of us for decades! But there are aspects of her personal life that illustrate her even more profound qualities. I will begin with a deeply moving anecdote in her early life that enhanced my admiration for her person in an immeasurable way. In the main part of the talk I will discuss three aspects of the initial value formulation (IVF) of general relativity that encompass dynamical black holes, null infinity, and the generalization of the formulation provided by the connection variables of loop quantum gravity. The first emphasizes constraint equations; the second, dynamical equations; and the third provides a generalization of the standard IVF that enable one to evolve across certain singularities, going beyond the standard Cauchy problem.
The talk is based on joint work on these three faces of the IVF with many colleagues, especially Badri Krishnan; Neev Khera; and Adam Henderson and David Sloan.
Badri Krishnan
TBA
Cécile Huneau
The global stability of the Kaluza-Klein spacetime
In this talk, I will present a recent work in collaboration with Annalaura Stingo and Zoe Wyatt, where we show the classical global stability, for Einstein equations, of the flat Kaluza–Klein spacetime, which corresponds to Minkowski spacetime in R1+4 with one direction compactified on a circle. We consider small perturbations which are allowed to vary in all directions including the compact direction. These perturbations lead to the creation of massless modes and Klein–Gordon modes. On the analytic side, this leads to a PDE system coupling wave equations to an infinite sequence of Klein–Gordon equations with different masses. The techniques we use are based purely in physical space using the vector field method.
Elena Giorgi
The nonlinear stability of black holes: an overview
Black holes are the most striking predictions of General Relativity and are by now understood to be fundamental objects in our universe. In this colloquium talk, I will provide an overview of their mathematical properties, in particular concerning their stability as solutions to the Einstein equation, and give a bird’s-eye view of recent proofs of their nonlinear stability.
Juan A. Valiente Kroon
Asymptotics in General Relativity: the role of spatial infinity
In this overview talk, I will discuss the relation between the asymptotic behaviour of the gravitational at null infinity and spatial infinity, the so-called problem of spatial infinity. I will argue that the conditions assumed by Penrose in his programme to study isolated systems in General Relativity are too restrictive to describe generic spacetimes. I will also discuss how a conformal approach to the study of the structure of spatial initiated by H. Friedrich offers the tantalising possibility of settling down the problem of spatial infinity, thus providing us with a full understanding of the way that Cauchy data determines the asymptotic behaviour of the gravitational field. I will present some applications of these ideas to the computation of asymptotic charges.
Lydia Bieri
From the initial value problem in GR to gravitational radiation and memory
Yvonne Choquet-Bruhat’s result of 1952 on the initial value problem for the Einstein equations has had a huge impact in General Relativity. This result also established the first proof that gravitational waves exist in the nonlinear theory; which had been debated after Albert Einstein in 1916 had found wave solutions for the linearized equations. In this talk, I will emphasize the importance of Yvonne’s work for the understanding of gravitational waves. Then we shall discuss some recent results on gravitational wave memory.
Mihalis Dafermos
Extremal and near-extremal black holes
TBA
Piotr Chruściel
Characteristic general relativity
I will review my work with Yvonne Choquet-Bruhat and Tim Paetz on the characteristic Cauchy problem in general relativity, and some recent progress on the topic.
Thomas Baumgarte
Predictability in Numerical Relativity: the Legacy of Yvonne Choquet-Bruhat
Even though Prof. Choquet-Bruhat probably does not consider herself a numerical relativist, her work has had a profound impact on the field. In this talk I will provide examples of this impact by demonstrating that many of the key ingredients in current numerical relativity formulations build directly on the approaches developed or adopted by her. I will motivate why the coordinate conditions chosen in many numerical relativity simulations differ from the harmonic coordinates commonly adopted in analytical work, and will argue that here, too, analytical insights provide intuition and guidance for advancing and understanding numerical relativity simulations.