Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Schwarzschild metric and the Friedmann equations from Newtonian
  Gravitational collapse   As is well known, the 0 - 0 component of the Schwarzschild space can be
obtained by the requirement that the geodesic of slowly moving particles match
the Newtonian equation. Given this result, we show here that the remaining
components can be obtained by requiring that the inside of a Newtonian ball of
dust matched at a free falling radius with the external space determines that
space to be Schwarzschild, if no pathologies exist. Also we are able to
determine that the constant of integration that appears in the Newtonian
Cosmology, coincides with the spatial curvature of the FLRW metric. These
results are of interest at least in two respects, one from the point of view of
its pedagogical value of teaching General Relativity without in fact using
Einstein's equation and second, the fact that some results attributed to
General Relativity can be obtained without using General Relativity indicates
that these results are more general than the particular dynamics specified by
General Relativity.

18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
2
The categories of this paper are: math
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys