Speaker: Prof. Juan A.Valiente-Kroon，School of Mathematical Sciences, Queen Mary, University of London

Inviter: 吴小宁

Title: Conformal scattering methods for the conformal Einstein field equations

Language: English

Time & Venue: 2026.02.12 19:00-20:00 Zoom会议：813 6243 1491 密码：272570

Abstract: In this talk I will discuss how methods from Melrose’s School of Geometric Scattering can be used, together with the conformal Einstein field equations and a gauge based on conformal invariants to obtain sharp statements about the asymptotic behaviour of asymptotically flat solutions to the vacuum Einstein field equations in the region of spacetime near null and spatial infinity. This approach, which combines asymptotic expansions computed with the aim of computer algebra with detailed estimates obtained through the positive commutator method within the framework of b-calculus allows to relate, in a precise way, the behaviour of the gravitational field near spatial and null infinity to the properties of Cauchy data. In particular, one can identify the pieces of the data responsible for the development of logarithmic singularities at the intersection of spatial infinity and null infinity —thus providing a detailed description of the formation of polyhomogeneous asymptotics from smooth data. It is hoped that the approach described in this contribution will allow to obtain a complete understanding of the so-called problem of spatial infinity in General Relativity —that is, an understanding the consequences of the singularity in the conformal structure of spacetime at spatial infinity due to the presence of a non-vanishing ADM mass.