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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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Beahvior of the solutions to the wave equation in compactified hyperboloidal slicing
Ivánek, Richard ; Ledvinka, Tomáš (advisor) ; Kofroň, David (referee)
In this bachelor thesis we discuss the effects of compactification and hyperboloidal slicing of spacetime in the numerical solution of wave equation primarily for their appli- cation in numerical relativity. The aim was to find the pros and cons of these concepts, to illustrate expected problems using diagrams and to rate the results obtained in spe- cific model problems. A brief explanation and demonstration of relevant numerical me- thods, hyperbolic Cauchy hypersurfaces, compactification and causal diagrams is a part of the thesis. As a conclusion, the effect of compactification and slicing on the accuracy of differential and integrational schemes was compared as well as the effect of discrete representation on the quality of initial data. 1
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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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