Multi-fractal analysis of the gravitational waves

Abstract

According the non-linear paradigm, been formulated by one of the authors of this paper in the last 1980th, all processes in open, non-linear, dynamical systems are very complex, non-linear, ultra-wideband or fractal ones.
As well as the transient gravitational wave signal generated by a black hole system merging to form a single black and observed on September 14, 2015 at 09:50:45 UTC by the two detectors of the Laser Interferometer Gravitational-Wave Observatory placed in Hanford and Livingston has strictly non-linear nature, the presence of fractal and multi-fractal properties in its time-domain structure is supposed to be quite possible. To investigate these properties, some modern methods of mono-fractal and multi-fractal analyzes are applied.
The transient gravitational wave signals received in Hanford and Livingston are found to be multi-fractal ones. Being the unique natural ultra-wideband processes with changing mean frequency, they had complex, non-stationary multi-fractal structure. The set of the corresponding numerical parameters for those signals are estimated and discussed.