HomeLast revision: Fri, 19-11-1999 (This page is under construction)
My general research interests lie in understanding the dynamical properties of the classical relativistic gravitational field equations put forward by Einstein in 1915, and all physical phenomena that can be adequately modelled in terms of them. The central project in this effort is to probe and reveal the intrinsic structure of the space of all solutions to this set of coupled quasi-linear partial differential equations. Recent work in this context I was involved with focuses exclusively on applications of classical general relativity that lie in the arena of cosmology. Those previous, and also current, investigations are targeted towards a clearer understanding -- preferably in geometrical terms -- of the generic physical features of spatially inhomogeneous cosmological models that have a simple perfect fluid matter source. The physics of spacetime geometries in this class provides a solid explanatory basis for such mainstream research areas in modern relativistic cosmology as, e.g., (i) the detailed modelling of the past, present, and future evolutionary history of the observable part of the Universe, (ii) the description of the dynamical formation of matter structures on all conceivable cosmological distance scales, (iii) the generation and propagation of gravitational radiation in the early Universe, and its interaction with intervening matter, or (iv) the nature of the boundary conditions that were effective near the classical cosmological initial singularity. All work in these directions I participated in (which is largely mathematical physics oriented) points inevitably to the important issue of what constitute appropriate cosmological distance scales suitable for the definition of an as yet unknown clearcut averaging procedure which will respect all physical/gravitational features that are essential in relativistic cosmology. Behind the averaging problem in relativistic cosmology stands the question of the genericity of those solutions to the gravitational field equations which allow for a period of spatially homogeneous and isotropic behaviour during some part of their dynamical existence. The standard model of relativistic cosmology for the past 35 years states that on scales of the order of the present Hubble distance the physical features of the observable part of the Universe are of such a kind. However, steadily growing amounts of data generated by a great number of present-day high-precision observational programmes indicate that this need not necessarily be the case. It is thus of considerable interest to expand current research efforts into the study of alternative cosmological models which show much wider physical complexity.
Besides taking qualitative analytic approaches in pursuit of the research programme outlined, I am increasingly interested in learning how to use and apply to the problems of relativistic cosmology various numerical approximation methods that have been discussed by a number of international research groups active in the field of numerical relativity. Major techniques put forward in this field, developed since the early 1990s particularly in the context of black hole physics, promise to be of relevance here as well. A symmetric hyperbolic $1+3$ orthonormal frame formulation of the relativistic gravitational field equations as applied to cosmology (and a normalised version thereof using dimensionless dynamical variables which is currently under development), which I gained experience with during my Ph.D and my recent postdoctoral studies, appears ideally suited for extensive numerical experiments. This kind of analysis, parallelling present major projects on numerically modelling the coalescence of binary black holes and the related generation of gravitational radiation, would support and extend the theoretical basis for analysing and interpreting data expected to be obtained throughout the next two decades by such gravitational radiation astronomy facilities as (amongst others) LIGO, VIRGO and GEO600 that are currently awaiting the completion of construction.
My further research interests concern the issue of a physically useful approach to describing the entropy intrinsic in (cosmological) gravitational fields, as well as the relation between dynamical models of features of the observable part of the Universe developed in relativistic cosmology and actual present-day and future astronomical observations. In view of the latter, measurements such as those that monitor the anisotropies in the cosmic microwave background radiation or research programmes dedicated to the study of gravitational lensing phenomena provide a major part of the information which is hoped to eventually lead us to a near-complete understanding of the physics of the observable part of the Universe.
Dr Henk van Elst
Postdoctoral Research Fellow
Cosmology Group
University of Cape Town
SOUTH AFRICA
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Last revision: Fri, 19-11-1999 (This page is under construction)