Nonlinear Gravitational Waves and Solitons
Gravitational wave astronomy is born in 2016. The laser interferometers of Advanced LIGO have detected two gravitational waves, each one generated by two black hole pairs. The observed wave profiles result from the fusion of two stellar-mass black holes into a single rotating black hole, with the emission of gravitational radiation with energy in the solar-mass scale. Indeed, they are the most violent astrophysical events recorded to date. Since gravitational waves solve the weak-field approximation of the Einstein equations in vacuum, in this limit, they evolve as linear waves. However, gravitational waves are intrinsically nonlinear waves; in fact, the chirp of the signal, the change in frequency observed by Advanced LIGO detectors, is due to the nonlinearity at the sources, even being negligible far away from them. Both cylindrical and planar nonlinear gravitational waves can be interpreted as soliton solutions of Einstein’s equations outside the sources. Actually, even black holes, the main sources of gravitational radiation, are two-soliton solutions of Einstein’s equations in vacuum. Gravitational solitons differ from standard nonlinear solitons in several aspects, including new phenomena such as multi-soliton coalescence, a phenomenon that emits low-amplitude radiation. Indeed, the pair-of-pants solution for the fusion of two black holes can be interpreted in such a way. In conclusion, although gravitational waves propagate in spacetime like linear waves, at their sources they are nonlinear gravitational waves and, even, gravitational solitons.
KeywordsGravitational waves Black holes Gravitational solitons Inverse scattering method
The author acknowledges financial support from project TIN2014-56494-C4-1-P from Programa Estatal de Fomento de la Investigación Científica y Técnica de Excelencia del Ministerio de Ciencia e Innovación (MICINN) of Spain.
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