Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Remarks on the geodesically completeness and the smoothing effect on
  asymptotically Minkowski spacetimes   In this note, we study a geometric property of asymptotically Minkowski
spacetimes and an analytic property of the Klein-Gordon operator. Precisely,
our first main results show that asymptotically Minkowski spacetimes are
geodesically complete under a null non-trapping condition. Secondly, we prove
that Sobolev index of a real principal type estimate used in the previous work
is actually optimal.

11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics