Nonlinear self-interaction of plane gravitational waves
Abstract
Recently Mendonca and Cardoso [Phys. Rev. D, vol. 66, 104009 (2002)] considered nonlinear gravitational wave packets propagating in flat space-time. They concluded that the evolution equation - to third order in amplitude - takes a similar form to what arises in nonlinear optics. Based on this equation, the authors found that nonlinear gravitational waves exhibit self-phase modulation and high harmonic generation leading to frequency up-shifting and spectral energy dilution of the gravitational wave energy. In this Brief Report we point out the fact - a possibility that seems to have been overlooked by Mendonca and Cardoso - that the nonlinear terms in the evolution equation cancels and, hence, that there is no amplitude evolution of the pulse. Finally we discuss scenarios where these nonlinearities may play a role.
Cite
@article{arxiv.astro-ph/0303412,
title = {Nonlinear self-interaction of plane gravitational waves},
author = {M. Servin and M. Marklund and G. Brodin and J. T. Mendonca and V. Cardoso},
journal= {arXiv preprint arXiv:astro-ph/0303412},
year = {2009}
}
Comments
2 pages, to appear in Phys. Rev. D