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No. of bitstreams: 1 MacksonMatheusFrancaNepomuceno_TESE.pdf: 12126877 bytes, checksum: 07d5c77235cdfd529f0902323ba9b8e0 (MD5) Previous issue date: 2016-12-12 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior (CAPES) / Usando as recentes observa??es da onda gravitacional GW150914 produzida pelo sistema de buracos negros bin?rios coalescentes, a presente tese investiga a natureza fractal e multifractal da varia??o temporal da deforma??o relativa (strain) medido pelos detectores do Observat?rio de Ondas Gravitacionais por Interferometria Laser (LIGO na sigla em ingl?s). Uma sele??o de m?todos e procedimentos, tais como as an?lises R/S e Wavelet, assim como, o m?todo multifractal denotado por MFDMA, foram usados para estimar par?metros estat?sticos que sintetizam a onda gravitacional como uma s?rie temporal complexa. Seja nos dados de Hanford ou Livingston, a an?lise fractal revelou que a referida s?rie apresenta um comportamento com forte persist?ncia e mem?ria de longa dura??o quantificado pelo expoente de Hurst. Al?m disso, a forte aglomera??o das flutua??es encontrados pela an?lise R/S indica o alto grau de depend?ncia por escala, caracter?stica de um sinal multifractal. Por outro lado, a an?lise multifractal atrav?s do m?todo MFDMA sugere que a s?rie temporal apresenta uma predomin?ncia de fracas singularidades em detrimentos ?s fortes, causando uma assimetria no espectro de singularidade D(h). Neste contexto, foram realizados dois tipos de procedimentos que analisam as poss?veis fontes de multifractalidade presentes na s?rie temporal. Os resultados mostram que procedimentos apontam para a exist?ncia de dois regimes de multifractalidade na s?rie temporal separados pela regi?o onde ocorre a colis?o dos buracos negros, referentes aos dados de Hanford, e, para os dados de Livingston, pr?ximo ao final da fase de inspiraliza??o. Em seguinte, foi verificado a evolu??o temporal dos par?metros multifractais, um processo similar ao adotado quando aplica-se a an?lise R/S. Como um resultado, constatou-se que, durante a evolu??o da diversidade lateral esquerda do espectro D(h), esse par?metro sofre um pequeno impulso. A origem f?sica desse impulso pode estar associada ? amplitude da mem?ria derivada do n?vel de polariza??o em rela??o a linha de visada do observador. Essa caracter?stica pode abrir caminho para uma gama de especula??es, dentre elas, que a elasticidade do tecido espa?o-tempo por ser inferida pelo comportamento multifractal da onda gravitacional. / 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.