Caracterização não-extensiva de ondas gravitacionais: o formalismo do q-tripleto de Tsallis

Abstract

The existence of gravitational waves was predicted by Einstein in 1916 as perturbations in the curvature of spacetime generated by accelerated masses. A century later, their direct detection by the LIGO interferometers inaugurated a new era in observational astrophysics. However, the complexity and inherently out-of-equilibrium nature of these signals challenge traditional statistical models based on Boltzmann–Gibbs entropy. In this context, this thesis proposes the application of Tsallis non-extensive statistical mechanics as a framework to describe and interpret gravitational-wave signals across multiple scales. This study investigates, through Tsallis non-extensive statistics, the multiscale structure of gravitational-wave signals originating from coalescing binary systems, relating the exponents of the q-triplet (qstat, qsen, qrel) to the physical parameters of the gravitational waves. The methodology is based on the analysis of publicly available time series from the Hanford and Livingston detectors, which were subjected to filtering, segmentation, and normalization procedures. The q-triplet exponents were obtained by: (i) fitting q-Gaussian distributions (qstat ); (ii) multifractal detrended fluctuation analysis (MF-DFA) to estimate qsen; and (iii) computation of average mutual information (AMI) to determine qrel. Pearson and Spearman correlation analyses, as well as linear regressions, were performed between the q-indices and the physical variables of the binary systems. For the GW150914 event, the estimated q-triplet values indicated strong non-extensivity: {1.46; 0.02; 2.28}H for Hanford and {1.43; 0.25; 2.26}L for Livingston. In the multi-event analysis, qsen exhibited a strong correlation with the peak frequency (R2=0.78) under linear fitting, while qrel showed a moderate correlation with the chirp mass (R2=0.26). In contrast, qstat did not present statistically significant correlations, suggesting the influence of stochastic factors. The application of Tsallis non-extensive statistics proved effective in characterizing the multiscale complexity and out-of-equilibrium behavior of gravitational-wave signals. The use of the q-triplet emerges as a promising approach for identifying distinct dynamical regimes during black hole coalescence processes, contributing new methodological perspectives to the astrophysics of extreme systems.