Natureza fractal e multifractal da onda gravitacional GW150914 detectada pelo LIGO

Abstract

Using the recent observations of the gravitational wave GW150914 produced by the binary black holes coalescing system, the present thesis investigates the fractal and multifractal nature of the temporal variation of the strain measured by the detectors of the Observatory of Gravitational Wave by Laser Interferometry-LIGO. A selection of methods and procedures, such as the R/S andWavelet analysis, as well as the multifractal method denoted by MFDMA, were used to estimate statistical parameters that synthesize the gravitational wave as a complex time series. Whether in the Hanford or Livingston data, the fractal analysis revealed that the series presents a behavior with strong persistence and long-term memory quantified by the Hurst exponent. In addition, the strong agglomeration of the fluctuations found by the R/S analysis indicates the high degree of scale dependence characteristic of a multifractal signal. On the other hand, multifractal analysis using the MFDMA method suggests that the time-series presents a predominance of weak singularities in detriments to the strong, causing an asymmetry in the singularity spectrum D(h). In this context, two types of procedures were performed that analyze the possible sources of multifractality present in the time-series. The results show that procedures point to the existence of two multifractality regimes in the time series separated by the region where the black holes collide, referring to the Hanford data, and, for the Livingston data, near the end of the inspiral phase. Then, the temporal evolution of the multifractal parameters was verified, a process similar to that adopted when applying the R/S analysis. As a result, it was found that, during the evolution of the left lateral diversity of the spectrum D(h), this parameter undergoes a small impulse. The physical origin of this pulse may be associated with the amplitude of the memory derived from the polarization level in relation to the observer’s line of sight. This feature may open the way for a range of speculations, among them, the elasticity of the space-time fabric to be inferred by the multifractal behavior of the gravitational wave.