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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: A review of the field of numerical relativity can be found in this article, where the authors describe the techniques most commonly used and discuss open problems and (some) future prospects for numerical simulations.
Abstract: Computer simulations are enabling researchers to investigate systems which are extremely difficult to handle analytically. In the particular case of general relativity, numerical models have proved extremely valuable for investigations of strong-field scenarios and been crucial in revealing unexpected phenomena. Considerable efforts are being spent to simulate astrophysically relevant simulations, understand different aspects of the theory and even provide insights into the search for a quantum theory of gravity. In this paper I review the present status of the field of numerical relativity, describe the techniques most commonly used and discuss open problems and (some) future prospects.
181 citations
TL;DR: In this paper, the authors summarize a recently proposed concrete program for investigating the (semi)classical limit of canonical, Lorentzian, continuum quantum general relativity in four spacetime dimensions.
180 citations
TL;DR: In this paper, a numerical method for general relativity and an application of that method are presented, which involves the use of harmonic coordinates in a 3+1 code to evolve the Einstein equations with scalar field matter.
Abstract: This paper presents both a numerical method for general relativity and an application of that method. The method involves the use of harmonic coordinates in a 3+1 code to evolve the Einstein equations with scalar field matter. In such coordinates, the terms in Einstein's equations with the highest number of derivatives take a form similar to that of the wave equation. The application is an exploration of the generic approach to the singularity for this type of matter. The preliminary results indicate that the dynamics as one approaches the singularity is locally the dynamics of the Kasner spacetimes.
176 citations
TL;DR: In this article, the second-order gravitational field and equations of motion for two point-like objects in algebraically closed form were obtained using a fast-motion approximation method and a regularization procedure was used to guarantee the consistency of the approximation scheme.
Abstract: Using a fast-motion approximation method we obtain the second-order gravitational field and equations of motion for two pointlike objects in algebraically closed form. A regularization procedure is used which is shown to guarantee the consistency of the approximation scheme. The equations of motion are then transformed within the framework of relativistic predictive mechanics into a system of ordinary differential equations.
169 citations