On the occurrence of gauge-dependent secularities in nonlinear gravitational waves

Briscese, Fabio and Santini, Paolo Maria (2017) On the occurrence of gauge-dependent secularities in nonlinear gravitational waves. Classical and Quantum Gravity, 34 (14). p. 144001. ISSN 0264-9381

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Official URL: https://doi.org/10.1088/1361-6382/aa7451

Abstract

We study the plane (not necessarily monochromatic) gravitational waves at nonlinear quadratic order on a flat background in vacuum. We show that, in the harmonic gauge, the nonlinear waves are unstable. We argue that, at this order, this instability can not be eliminated by means of a multiscale approach, i.e. introducing suitable long variables, as is often the case when secularities appear in a perturbative scheme. However, this is a non-physical and gauge-dependent effect that disappears in a suitable system of coordinates. In fact, we show that in a specific gauge such instability does not occur, and that it is possible to solve exactly the second order nonlinear equations of gravitational waves. Incidentally, we note that this gauge coincides with the one used by Belinski and Zakharov to find exact solitonic solutions of Einstein's equations, that is to an exactly integrable case, and this fact makes our second order nonlinear solutions less interesting. However, the important warning is that one must be aware of the existence of the instability reported in this paper, when studying nonlinear gravitational waves in the harmonic gauge.

Item Type: Article
Uncontrolled Keywords: nonlinear gravitational waves, stability of gravitational waves, secular equations
Subjects: F300 Physics
G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics and Information Sciences
Depositing User: Paul Burns
Date Deposited: 28 Jul 2017 10:16
Last Modified: 28 Jul 2017 10:29
URI: http://nrl.northumbria.ac.uk/id/eprint/31413

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