A geometric choice of asymptotically Euclidean coordinates via STCMC-foliations

Abstract: Asymptotically Euclidean initial data sets (IDS) in General Relativity model instants in time for isolated systems. In this talk, we show that an IDS is asymptotically Euclidean if it admits a cover by closed hypersurfaces of constant spacetime mean curvature (STCMC), provided these hypersurfaces satisfy certain geometric estimates, some weak foliation properties, and each surface exhibits generalized stability. Building on the work of Cederbaum and Sakovich (2021), which established that every asymptotically Euclidean IDS has a unique STCMC foliation, we conclude that the existence of such a foliation characterizes asymptotically Euclidean IDS. Furthermore, we explore the connections to the center of mass and show why these coordinates seem well-adapted to describe this concept. This is joint work with O. Vičánek Martínez.

general relativity and quantum cosmologymathematical physicsanalysis of PDEsdifferential geometry

Audience: researchers in the topic

( video )

---

JoMaReC - Joint Online Mathematical Relativity Colloquium

Series comments: This monthly online colloquium is meant to be accessible to and informative for mathematicians and mathematical physicists with a background in General Relativity, widely interpreted to include Lorentzian Geometry, and Geometric Analysis of various Partial Differential Equations related to General Relativity.

It is aimed to present motivation and applications of particular results and/or introduce specific subfields, while refraining from too much technicalities.

---