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Review of 'Orbital effects of a monochromatic plane gravitational wave with ultra-low frequency incident on a gravitationally bound two-body system'

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5
This is a very good paper which deserved publication in ScienceOpen.
Average rating:
    Rated 5 of 5.
Level of importance:
    Rated 5 of 5.
Level of validity:
    Rated 5 of 5.
Level of completeness:
    Rated 5 of 5.
Level of comprehensibility:
    Rated 4 of 5.
Competing interests:
The reviewer and the author of this article have co-authored four publications between 2009-2013.

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Orbital effects of a monochromatic plane gravitational wave with ultra-low frequency incident on a gravitationally bound two-body system

 Lorenzo Iorio (2014)
We analytically compute the long-term orbital variations of a test particle orbiting a central body acted upon by an incident monochromatic plane gravitational wave. We assume that the characteristic size of the perturbed two-body system is much smaller than the wavelength of the wave. Moreover, we also suppose that the wave's frequency νg is much smaller than the particle's orbital one nb. We make neither a priori assumptions about the direction of the wavevector k nor on the orbital configuration of the particle. While the semi-major axis a is left unaffected, the eccentricity e, the inclination I, the longitude of the ascending node Ω, the longitude of pericenter ϖ and the mean anomaly ℳ undergo non-vanishing long-term changes of the form dΨ/dt=F(Kij;e,I,Ω,ω),Ψ=e,I,Ω,ϖ,M, where Kij, i,j=1,2,3 are the coefficients of the tidal matrix K. Thus, in addition to the variations of its orientation in space, the shape of the orbit would be altered as well. Strictly speaking, such effects are not secular trends because of the slow modulation introduced by K and by the orbital elements themselves: they exhibit peculiar long-term temporal patterns which would be potentially of help for their detection in multidecadal analyses of extended data records of planetary observations of various kinds. In particular, they could be useful in performing independent tests of the inflation-driven ultra-low gravitational waves whose imprint may have been indirectly detected in the Cosmic Microwave Background by the Earth-based experiment BICEP2. Our calculation holds, in general, for any gravitationally bound two-body system whose orbital frequency nb is much larger than the frequency νg of the external wave, like, e.g., extrasolar planets and the stars orbiting the Galactic black hole. It is also valid for a generic perturbation of tidal type with constant coefficients over timescales of the order of the orbital period of the perturbed particle.
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    Review information

    10.14293/S2199-1006.1.SOR-ASTRO.AWXWIL.v1.RKXGOE

    This work has been published open access under Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com.

    Review text

    In this paper the author computes the long-term orbital variations of a test particle orbiting a central body acted upon by an incident monochromatic plane gravitational wave under the assumption that the wave is “frozen” with respect to the astrophysical observations. This assumption is justified from a phenomenological point of view because if one applies the author's results to the solar system it will be possible, in principle, to put constraints over a part of the ultra-low frequency spectrum of gravitational waves for which neither ground-based nor space-based dedicated experimental devices are available. This is a very important observation which, even if taken alone, justifies the importance of this paper.
    More in general, the paper is well written and looks mathematically consistent. I stress also the importance of the presented results in cosmology because the resulting bounds can be considered independent tests on relic gravitational waves that the BICEP2 collaboration claimed to have recently detected. The author also recalls other different approaches to study the same problem discussed in the present paper. I have no doubts that this is a very good paper which deserved publication in ScienceOpen. I have only a minor suggestion in order to clarify a issue that could be, in principle, misleaded. Page 2, the sentence below eq. (3) “The fact that both^{7} h_{00} and h_{0i}, i=1,2,3 vanish in the transverse traceless (TT) gauge [76], which is tacitly assumed here^{8}” can mislead and must be modified. In fact, the (TT) coordinates are slightly different from the local inertial Fermi coordinates. The coordinate transform can be indeed found in D. Baskaran and L. P. Grishchuk, Class. Quant. Grav. 21 4041 (2004) and its generalization to scalar waves in C. Corda, Phys. Rev. D83, 062002 (2011). Thus, I suggest to re-write the sentence in a way similar to the following: “As the linarized Rienmann tensor is gauge-invariant [76], one can compute h_{00} and h_{0i}, i=1,2,3 directly in the transverse traceless (TT)^{7} gauge [76] finding that they vanish”. The author should also remove note ^{8} accordingly.

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