Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Towards a theory of nonlinear gravitational waves: a systematic approach
  to nonlinear gravitational perturbations in vacuum   We present a systematic and robust approach to nonlinear gravitational
perturbations of vacuum spacetimes. This approach provides a basis for a theory
of nonlinear gravitational waves. In particular, we show that the system of
perturbative Einstein equations reduces at each perturbation order to two (for
each gravitational mode in 3 + 1 dimensions on which our study is focused)
scalar wave equations, and then we show how the metric perturbations can be
explicitly obtained, once the solutions to these scalar wave equations are
known. These results show that the concept of polarization of a gravitational
wave does make sense also beyond the linear approximation.

28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin