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Nonlinear self-interaction of plane gravitational waves

M. Servin·M. Marklund·G. Brodin·J. T. Mendonca·V. Cardoso
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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.

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M. Servin, M. Marklund, G. Brodin, J. T. Mendonca, V. Cardoso. 2003-03-18. Nonlinear self-interaction of plane gravitational waves. https://doi.org/10.1103/physrevd.67.087501

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