Talk page
Title:
Coordinates are messy
Speaker:
Abstract:
Asymptotically Euclidean initial data sets $(M,g,K)$ are characterized by the existence of asymptotic coordinates in which the Riemannian metric $g$ and second fundamental form $K$ decay to the Euclidean metric $\delta$ and to $0$ suitably fast, respectively. Provided their matter densities satisfy suitable integrability conditions, they have well-defined (ADM-)energy, (ADM-)linear momentum, and (ADM-)mass as was shown by Bartnik in 1986. To study their (ADM-)angular momentum and (BORT-)center of mass, one usually assumes the existence of so-called Regge—Teitelboim coordinates. We will give examples of asymptotically Euclidean initial data sets which do not possess any Regge—Teitelboim coordinates and explain other “non-features” of the Regge—Teitelboim coordinate conditions. This is joint work with Melanie Graf and Jan Metzger. We will also explain the consequences of these findings for the definition of the center of mass, relying on joint work with Nerz and with Sakovich.
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