Following up the First Detection of Gravitational Waves with Numerical Relativity Simulations

Abstract

[eng] The first detection of a gravitational wave signal occurred on September 14 2015, when the two LIGO detectors in Hanford and Livingston registered a consistent signal with a statistical significance of more than 5! relative to the background noise. In order to identify the source of gravitational wave signals, they need to be compared with theoretical predictions. In the case of the first detection, the signal was found consistent with the prediction of general relativity for the waves produced by the last orbits and coalescence of two black holes with initial masses 36M! and 29M!, leading to a final black hole mass of 62M! with 3.0M!c2 radiated in gravitational waves. The modern theory of gravitation is Einstein’s theory of general relativity, and modelling possible signals with solutions of the Einstein equations is a key goal for gravitational wave physics. Perturbative methods, as have been used for the indirect discovery by Hulse, Taylor, and Weisberg [1, 2] of gravitational wave emission from the binary pulsar PSR B1913+16 in 1974, break down in the strong field regime of general relativity, and to model the merger of black holes, the methods of numerical relativity to solve the Einstein equations without physical approximations need to be used. In this thesis a precessing waveform compatible with the first detection event, GW150914, is constructed by numerical solution of the Einstein field equations as a system of coupled nonlinear partial di↵erential equations, and compared with the data recorded by the LIGO detectors. Perturbative methods are used to compute initial parameters for the black holes, and to construct a complete waveform by matching the numerical and perturbative solutions. Physical properties of the solution are computed and discussed, such as the final spin, final mass, recoil velocity and energy distribution for di↵erent spherical harmonic modes of the wave signal. The Einstein evolution equations can be considered a nonlinear system of wave equations, and the numerical solution of the linear wave equation is discussed to introduce the numerical finite di↵erence methods used.