Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Closed time like curve and the energy condition in 2+1 dimensional
  gravity   We consider gravity in 2+1 dimensions in presence of extended stationary
sources with rotational symmetry. We prove by direct use of Einstein's
equations that if i) the energy momentum tensor satisfies the weak energy
condition, ii) the universe is open (conical at space infinity), iii) there are
no CTC at space infinity, then there are no CTC at all.

18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an