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[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. |
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