Simulation of gravitational waves and binary black holes space-times
Examensarbete för masterexamen
The main objective of this thesis is to study gravitational radiation along with its associated phenomena, specifically for binary black holes. The occurrence of such events in our universe have profound implications when gravitational waves are radiated by accelerating massive astrophysical bodies. The specific system under our consideration is a binary black hole. The two essential phases of binary black hole, namely inspiral and merger have their characteristic gravitational wave signature. Gravitational waves during these phases are obtained by taking advantage of powerful numerical tools available. Two popular techniques are applied to determine waveforms, namely post-Newtonian approximation for the inspiral phase and numerical relativity techniques for the merger phase of binaries. The nature of gravitational wave is explained by considering the linearised theory of general relativity and its effect on free-falling bodies. A detailed description of the multipole expansion is provided which also encompasses the famous Einstein quadrupole formula. For the inspiral phase of binary black holes, the post-Newtonian formalism is discussed in detail. Extraction of waveforms by the post-Newtonian method is implemented by MATLAB routines to test the findings. Lastly, the foundation of numerical relativity is reviewed which serves the purpose to carry out further discussions on gravitational waves in strong gravity regime during merger phase of binaries. ADM and BSSN formalism is introduced along with the Schwarzschild and Misner initial data. BSSN evolution of Misner initial data is carried out by CCATIE code. The Weyl scalars are extracted to provide an invariant way of representing outgoing gravity waves at various stages of evolution.
Astronomi, astrofysik och kosmologi , Astronomy, Astrophysics and Cosmology