Uma perspectiva não-extensiva da estrutura multi-escala das flutuações presente na onda gravitacional GW150914

Abstract

The recent gravitational waves detections observed by the Gravitational Wave Observatory by Laser Interferometer (LIGO) are used in this work to investigate fluctuations in gravitational waves when the binary system goes into the coalescence process. Thus, time series were constructed from the data of measurement of strain relative deformation caused by the gravitational wave GW150914, first detected by LIGO. Hence, the entropic index q was used, emerged from the non-extensive statistical mechanics developed by C. Tsallis, to characterize the multiscale structure of fluctuations. It is known that there are two types of memory present in a gravitational wave: one of nonradiative origin and one of radiative origin that presents frequencies over the instrumental detection limit of the LIGO and, therefore, have not yet been detected experimentally. This nonlinear character is associated with the memory of Christodoulou arising from an electromagnetic correction of the expansion of Multipoles. Thus, one sought with the aforementioned statistical theory to verify the behavior of theentropic index and to map phase transition regions that can quantify the phenomenon and possibly correlate it with properties inherent to the physics of the gravitational wave. In this sense, the study is based on the idea that there are fluctuations in which the radiative gravitational memory can be manifested. Thus, the result in the Hanford detector indicated that for the gravitational wave GW150914, a phase transition occurs at the maximum value of q, with a corresponding time of 7.75 ms (millisecond) and, therefore, a frequency of 130 Hz. On the Livingston detector, for the maximum value of q, the corresponding time of 3.85 ms (millisecond) and, therefore, a frequency of 260 Hz. At maximum frequencies, a strong non-extensive effect can be associated with the coalescence of black holes. In frequencies higher than 130 Hz and 260 Hz, the regime becomes extensive, that is, the system is in the state of thermodynamic equilibrium. Initially, this result reveals that the radiative memory is present in the process of inspiraling the binary system of black holes. Therefore, it is believed that the region where the phase transition is measured is not a statistical artifact, but a physical manifestation provoked by the mechanisms that precede the fusion of black holes.