Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Compact Four-Dimensional Euclidean-Space Immersed in the Universe   A compact four-dimensional manifold whose metric tensor has a positive
determinant (named the "Euclid ball") is considered. The Euclid ball can be
immersed in the Minkovskian space (which has the negative determinant) and can
exist stably through the history of the universe. Since the Euclid ball has the
same solution as the Schwarzschild black hole on its three-dimensional surface,
an asymptotic observer can not distinguish them. If large fraction of whole
energy of the pre-universe was encapsulated in Euclid balls, they behave as the
dark matter in the current universe. Euclid balls already existed at the end of
the cosmological inflation, and can have a heavy mass in this model, they can
be a seed of supper-massive black-holes, which are necessary to initiate a
forming of galaxies in the early universe. The $\gamma$-ray burst at early
universe is also a possible signal of the Euclidean ball.

32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph