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This thesis is concerned with the development and application of conformaltechniques to numerical calculations of asymptotically flat spacetimes. Theconformal compactification technique enables us to calculate spatiallyunbounded domains, thereby avoiding the introduction of an artificial timelikeouter boundary. We construct in spherical symmetry an explicit scri-fixinggauge, i.e. a conformal and a coordinate gauge in which the spatial coordinatelocation of null infinity is independent of time so that no resolution loss inthe physical part of the conformal extension appears. Going beyond sphericalsymmetry, we develop a method to include null infinity in the computationaldomain. With this method, hyperboloidal initial value problems for the Einsteinequations can be solved in a scri-fixing general wave gauge. To study spatialinfinity, we discuss the conformal Gauss gauge and the reduced generalconformal field equations from a numerical point of view. This leads us to thefirst numerical calculation of the entire Schwarzschild-Kruskal solutionincluding spatial, null and timelike infinity and the domain close to thesingularity. After developing a three dimensional, frame based evolution codewith smooth inner and outer boundaries we calculate a radiative axisymmetricvacuum solution in a neighbourhood of spatial infinity represented as acylinder including a piece of null infinity. In this context, a certaincomponent of the rescaled Weyl tensor representing the radiation field iscalculated unambiguously with respect to an adapted tetrad at null infinity.

A conformal approach to numerical calculations of asymptotically flat spacetimes