2007/11/06 by Anıl Zenginoğlu, Zenginoğlu, Anıl · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Pulsars and Gravitational Waves Research
paper · pdf · doi:10.48550/arxiv.0711.0873
openalex publication_date 2007/11/06 · openalex created_date 2022/08/31 · openalex updated_date 2026/07/28
This thesis is concerned with the development and application of conformal\ntechniques to numerical calculations of asymptotically flat spacetimes. The\nconformal compactification technique enables us to calculate spatially\nunbounded domains, thereby avoiding the introduction of an artificial timelike\nouter boundary. We construct in spherical symmetry an explicit scri-fixing\ngauge, i.e. a conformal and a coordinate gauge in which the spatial coordinate\nlocation of null infinity is independent of time so that no resolution loss in\nthe physical part of the conformal extension appears. Going beyond spherical\nsymmetry, we develop a method to include null infinity in the computational\ndomain. With this method, hyperboloidal initial value problems for the Einstein\nequations can be solved in a scri-fixing general wave gauge. To study spatial\ninfinity, we discuss the conformal Gauss gauge and the reduced general\nconformal field equations from a numerical point of view. This leads us to the\nfirst numerical calculation of the entire Schwarzschild-Kruskal solution\nincluding spatial, null and timelike infinity and the domain close to the\nsingularity. After developing a three dimensional, frame based evolution code\nwith smooth inner and outer boundaries we calculate a radiative axisymmetric\nvacuum solution in a neighbourhood of spatial infinity represented as a\ncylinder including a piece of null infinity. In this context, a certain\ncomponent of the rescaled Weyl tensor representing the radiation field is\ncalculated unambiguously with respect to an adapted tetrad at null infinity.\n