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Introduction to the mathematics of general relativity
About: Introduction to the mathematics of general relativity is a research topic. Over the lifetime, 2583 publications have been published within this topic receiving 73295 citations.
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TL;DR: In this article, a family of symmetric hyperbolic initial-boundary value formulations for the linearized Einstein equations is analyzed using the Laplace-Fourier technique.
Abstract: A persistent challenge in numerical relativity is the correct specification of boundary conditions. In this work we consider a many-parameter family of symmetric hyperbolic initial-boundary value formulations for the linearized Einstein equations and analyze its well posedness using the Laplace–Fourier technique. By using this technique ill posed modes can be detected and thus a necessary condition for well posedness is provided. We focus on the following types of boundary conditions: (i) boundary conditions that have been shown to preserve the constraints, (ii) boundary conditions that result from setting the ingoing constraint characteristic fields to zero, and (iii) boundary conditions that result from considering the projection of Einstein’s equations along the normal to the boundary surface. While we show that in case (i) there are no ill posed modes, our analysis reveals that, unless the parameters in the formulation are chosen with care, there exist ill posed constraint violating modes in the remaining cases.
36 citations
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35 citations
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01 Jan 1975
35 citations
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01 Jan 2010TL;DR: The special theory of relativity as mentioned in this paper has been applied to the general theory of general relativity in a wide range of applications, e.g. in the field of astrophysics, astronomy, and cosmology.
Abstract: 1. The special theory of relativity 2. From special to the general theory of relativity 3. Vectors and tensors 4. Covariant differentiation 5. Curvature of spacetime 6. Spacetime symmetries 7. Physics in curved spacetime 8. Einstein's equations 9. The Schwarzschild solutions 10. Experimental tests of general relativity 11. Gravitational radiation 12. Relativistic astrophysics 13. Black holes 14. The expanding universe 15. Friedmann models 16. The early universe 17. Observational cosmology 18. Beyond relativity References Index.
35 citations