Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Einstein's equation is incompatible with a Galilean limit in
  non-Euclidean spatial classes of topologies   We show that the Galilean limit of Lorentzian structures applied to a
solution of the Einstein equation only exists if the topological class (i.e.
Thurston's geometric structure) of the spatial sections of the spacetime
4-manifold is Euclidean. We argue that this result might be a signature of an
incompleteness of the Einstein equation, which should feature an additional
"topological term" linked to the spatial topological class. This term would
imply that the limit exists in any topological class. However, the term is only
known at the leading order of the Galilean limit, and remains unconstrained at
full order. We propose strategies to determine this topological term. If indeed
such a term is a missing feature of general relativity, the Einstein equation
in its current form would be physically incorrect if the Universe has a
non-Euclidean spatial topology.

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The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph