Is general relativity `essentially understood' ?
arXiv:gr-qc/0508016 · doi:10.1002/andp.200510173
Abstract
The content of Einstein's theory of gravitation is encoded in the properties of the solutions to his field equations. There has been obtained a wealth of information about these solutions in the ninety years the theory has been around. It led to the prediction and the observation of physical phenomena which confirm the important role of general relativity in physics. The understanding of the domain of highly dynamical, strong field configurations is, however, still quite limited. The gravitational wave experiments are likely to provide soon observational data on phenomena which are not accessible by other means. Further theoretical progress will require, however, new methods for the analysis and the numerical calculation of the solutions to Einstein's field equations on large scales and under general assumptions. We discuss some of the problems involved, describe the status of the field and recent results, and point out some open problems.
Extended version of a talk which was to be delivered at the DPG Fruehjahrstagung in Berlin, 5 March 2005
References in corpus (7)
- Numerical Relativity Using a Generalized Harmonic Decomposition
- Rough Solutions of the Einstein Constraint Equations on Compact Manifolds
- Gluing Initial Data Sets for General Relativity
- A model problem for the initial-boundary value formulation of Einstein's field equations
- A new geometric invariant on initial data for Einstein equations
- Time asymmetric spacetimes near null and spatial infinity. II. Expansions of developments of initial data sets with non-smooth conformal metrics
- Algebraic stability analysis of constraint propagation
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- Mathematical Issues in a Fully-Constrained Formulation of Einstein Equations
- From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
- Initial boundary value problems for Einstein's field equations and geometric uniqueness
- An introduction to local Black Hole horizons in the 3+1 approach to General Relativity
- Strong coupling expansion for general relativity