Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finding Schwarzschild metric component grr and FLRW's k without solving
  the Einstein's equation, rather by a synergistic matching between geometric
  results enfranchised by Newtonian gravity   As is well known, some aspects of General Relativity and Cosmology can be
reproduced without even using Einstein's equation. As an illustration, the 0 -
0 component of the Schwarzschild space can be obtained by the requirement that
the geodesic of slowly mov- ing particles match the Newtonian equation. Given
this result, we shall show here that the remaining component (grr) can be
obtained by requiring that the inside of a Newtonian ball of dust matched at a
free falling radius with the external space of unspecified type. This matching
determines the external space to be of Schwarzschild type. By this, it is also
possi- ble to determine that the constant of integration that appears in the
Newtonian Cosmology, coincides with the spatial curvature of the FLRW metric.
All we assumed was some classical boundary conditions and basic assumptions.

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The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph