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Numerical Relativity: 3+1 Formalism, Numerical Extraction of Gravitational Waves

Khalvati, Hassan | 2019

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 53089 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Rahvar, Sohrab
  7. Abstract:
  8. Einstein's theory of General Relativity is the cornerstone in many modern physics areas in which the strong gravitational field is engaged, i.e. modern cosmology, neutron star and black hole physics, generation of gravitational waves, and several other cosmic phenomena. Despite its simple appearance, the theory of general relativity is practically rigorous. Einstein's field equations are consist of 10 coupled, non-linear, partial differential equations in 4 space-time dimensions. Except for some highly symmetric space-times, general relativity does not provide exact analytical solutions to real problems with a low level of symmetry, since the field equations would be strongly complex for such systems. The necessity of studying systems real physical systems in the strong-gravity regime, with low, or even no symmetries, has led to the emergence of the Numerical Relativity, which tries to solve Einstein's field equations using complex numerical approaches.During this thesis, we introduce the motivations and the challenges in the field of Numerical Relativity. In addition to reviewing the 3+1 formalism, which is the basis of calculations in numerical relativity, we also study the methods of producing initial data for an arbitrary physical scenario in general relativity, and the suitable gauge choices in 3+1 formalism, in order to have a successful numeric simulation. Moreover, we have studied a common method of gravitational wave information extraction, using Newman-Penrose formalism, and Weyl scalars.Finally, we have used the most comprehensive, well-known gadget for numerical simulation of gravitational systems in numerical relativity, the Einstein toolkit, to simulate the evolution of a binary black holes system and extract physical gravitational wave information from that. The results are provided in the last chapter of this thesis
  9. Keywords:
  10. Numerical Relativity ; Gravitational Waves ; Simulation ; Black Holles ; Weyl Anomaly ; 3+1 Formalism ; Weyl Scalars ; Binary Black Holes ; Quasi-Kinnersley Tetrad

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