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Numerical evolution of black-hole spacetimes
Khirnov, Anton ; Ledvinka, Tomáš (advisor) ; Palenzuela, Carlos (referee)
吀e so-called "trumpet" initial data has recently received mu挀 a琀ention as a potential candidate for the natural black hole initial data to be used in 3+1 numerical relativity simulations with 1+log foliation. In this work we first derive a variant of the maximal trumpet initial data that is made to move on the numerical grid by the means of a Lorentz boost and write a numerical code that constructs this boosted trumpet initial data. We also write a numerical code for calculating the Krets挀mann scalar from the 3+1 variables, to be used in analysing the data from our simulations. With the help of those two codes, we study the behaviour of the boosted trumpet initial data when evolved with the BSSN formulation of the Einstein equations, using 1+log slicing and the Γ-driver shi昀 condition.
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Representation of dynamical black hole spacetimes in numerical simulations
Khirnov, Anton ; Ledvinka, Tomáš (advisor) ; Hilditch, David (referee) ; Liebling, Steven L. (referee)
Choptuik's unexpected discovery, almost 30 years ago, of critical behavior in grav- itational collapse opened a whole new research area within numerical relativity. While critical collapse in spherical symmetry has been thoroughly investigated and is reasonably well understood, progress for axial symmetry has been much slower. In this thesis, we study axially symmetric gravitational collapse of gravi- tational waves using numerical simulations. We construct several very different initial data families and investigate their behavior close to the threshold of collapse. We compare them against each other and also against other published results. We use invariant quantities to look for signs of self-similarity and universality.
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Numerical evolution of black-hole spacetimes
Khirnov, Anton ; Ledvinka, Tomáš (advisor) ; Palenzuela, Carlos (referee)
吀e so-called "trumpet" initial data has recently received mu挀 a琀ention as a potential candidate for the natural black hole initial data to be used in 3+1 numerical relativity simulations with 1+log foliation. In this work we first derive a variant of the maximal trumpet initial data that is made to move on the numerical grid by the means of a Lorentz boost and write a numerical code that constructs this boosted trumpet initial data. We also write a numerical code for calculating the Krets挀mann scalar from the 3+1 variables, to be used in analysing the data from our simulations. With the help of those two codes, we study the behaviour of the boosted trumpet initial data when evolved with the BSSN formulation of the Einstein equations, using 1+log slicing and the Γ-driver shi昀 condition.
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