Geometrically defined asymptotic coordinates in general relativity

In this project we study geometrically defined asymptotic foliations of initial data sets in General Relativity. They allow the
construction of asymptotic coordinate systems which are well adapted to the study of physical invariants such as mass and the center of mass. The type of foliations under consideration includes surfaces of constant mean curvature, constant expansion, and constant spacetime mean curvature.

The main goals of this project are:

Compare the different foliations and their related coordinate systems. Of particular interest is the influence of the value of physical invariants on the shape and position of the surfaces.
Of particular interest is to find coordinate systems that do not depend on the choice of initial data sets for a given space-time. This could in particular lead to coordinate independent versions of the Regge-Teitelboim asymptotic parity conditions.
Do all of the above this with as general asymptotic conditions as possible.

Publications

Carla Cederbaum, Melanie Graf: Coordinates are messy -- not only in General Relativity (2023)

The coordinate freedom of General Relativity makes it challenging to find mathematically rigorous and physically sound definitions for physical quantities such as the center of mass of an isolated gravitating system. We will argue that a similar phenomenon occurs in Newtonian Gravity once one ahistorically drops the restriction that one should only work in Cartesian coordinates when studying Newtonian Gravity. This will also shed light on the nature of the challenge of defining the center of mass in General Relativity. Relatedly, we will give explicit examples of asymptotically Euclidean relativistic initial data sets which do not satisfy the Regge--Teitelboim parity conditions often used to achieve a satisfactory definition of center of mass. These originate in our joint work with Jan Metzger. This will require appealing to Bartnik's asymptotic harmonic coordinates.

Publisher	Springer
Book	Gravity, Cosmology, and Astrophysics A Journey of Exploration and Discovery with Female Pioneers
	Link to preprint version
	Link to published version

Carla Cederbaum, Sophia Jahns: Correction to: Geometry and topology of the Kerr photon region in the phase space (2019)