Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Time evolution of ADM and CMC center of mass in general relativity   It is shown by several authors going back to Huisken-Yau that asymptotically
Schwarzschildean time-slices possess a unique foliation by stable constant mean
curvature (CMC) spheres defining the so-called CMC center of mass. We analyze
how the leaves of this foliation evolve in time under the Einstein equations.
More precisely, we prove that, asymptotically, their time evolution is a
translation induced by the quotient of their linear momentum and mass, as to be
expected from the corresponding Newtonian setting. In particular, the
definitions of mass and linear momentum defined by Arnowitt-Deser-Misner (ADM)
are compatible with the interpretation of the CMC foliation as the center of
mass of the time-slice by Huisken-Yau. Furthermore, we prove that the
coordinate version of the center of mass by Arnowitt-Deser-Misner and the
coordinate version of the CMC center of mass coincide - without additional
conditions on the scalar curvature. This is even true in the sense of
existence, i.e. if one of the two exists then so does the other.

21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph