Multi-fractal analysis of the gravitational waves

Leonid F. Chernogor Space Radio Physics Department V. N. Karazin Kharkiv National University Kharkiv, Ukraine
Oleg V. Lazorenko General Physics Department V. N. Karazin Kharkiv National University Kharkiv, Ukraine
Andryi A. Onishchenko Physics Department Kharkiv National University of Radioelectronics Kharkiv, Ukraine

Keywords: gravitational wave signal, mono-fractal analysis, multi-fractal analysis, non-linear paradigm, ultra-wideband process, multi-fractal structure

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.

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www.project.inria.fr/fraclab/.р