Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Corrections to the gravitational wave phasing   The gravitational wave, traveling a long cosmological distance to reach
interferometers, interacts with the (homogeneous and isotropic) cosmological
background, so generally speaking, its amplitude and phase are modified in some
nontrivial way. As the sensitivity of interferometers is improved, one may
detect corrections to the short-wavelength approximation, which naturally
includes the information of cosmological evolution. In this work, the
Newman-Penrose variable $\Psi_4$ has been calculated to show that there are two
new corrections to the short-wavelength approximation. One formally occurs at
the first post-Newtonian order but is highly suppressed by the Hubble
parameters; the other occurs at the fifth post-Newtonian order, which is due to
the variation of the amplitude. The first correction contains the evolution of
the Universe, but it may not be easily detected. The second one indicates that
the short-wavelength approximation has to be corrected, when the more accurate
waveforms with the higher-order post-Newtonian terms are calculated.

23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th