Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Concerning the instantaneous mass and the extent of an expanding
  universe   In this article we want to answer the cosmologically relevant question what,
with some good semantic and physical reason, could be called the mass of an
infinitely extended, homogeneously matter-filled and expanding universe. To
answer this question we produce a space-like sum of instantaneous cosmic energy
depositions surrounding equally each spacepoint in the homogeneous universe. We
calculate the added-up instantaneous cosmic energy per volume around an
arbitrary space point in the expanding universe. To carry out this sum we use
as basic metrics an analogy to the inner Schwarzschild metric applied to stars,
but this time applied to the spacepoint-related universe. It is then shown that
this leads to the added-up proper energy within a sphere of a finite outer
critical radius defining the point-related infinity. As a surprise this radius
turns out to be reciprocal to the square root of the prevailing average cosmic
energy density. The equivalent mass of the universe can then also be calculated
and, by the expression which is obtained here, shows a scaling with this
critical radius of this universe, a virtue of the universe which was already
often called for in earlier works by E.Mach, H.Thirring and F.Hoyle and others.
This radius on the other hand can be shown to be nearly equal to the
Schwarzschild radius of the so-defined mass of the universe.

1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph