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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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01 Jan 2013
TL;DR: The Lorentz transformation as discussed by the authors has been used for the conservation of energy-momentum and the principle of equivalence in the relation between different dimensions of spacetime. But it has not yet been applied to general relations.
Abstract: PART I: THE RELATIVISTIC WORLD 1. Basic ideas 2. The Lorentz transformation 3. Moving light sources 4. Dynamics 5. The conservation of energy-momentum 6. Further kinematics 7. Relativity and electromagnetism 8. Electromagnetic radiation PART II: AN INTRODUCTION TO GENERAL RELATIVITY 9. The Principle of Equivalence 10. Warped spacetime 11. Physics from the metric PART III: FURTHER SPECIAL RELATIVITY 12. Tensors and index notation 13. Rediscovering electromagnetism 14. Lagrangian mechanics 15. Angular momentum 16. Energy density 17. What is spacetime?

30 citations

01 Jan 1972

30 citations

Journal ArticleDOI
TL;DR: In this paper, a decoupling of the geometrical spatial curvature term in the metric from the dynamical spatial curvatures in the Friedmann equation was investigated by fitting to a combination of HST, CMB, type Ia supernovae (SNIa), and baryon acoustic oscillation (BAO) data sets.
Abstract: Averaging in general relativity is a complicated operation, due to the general covariance of the theory and the nonlinearity of Einstein's equations. The latter of these ensures that smoothing spacetime over cosmological scales does not yield the same result as solving Einstein's equations with a smooth matter distribution, and that the smooth models we fit to observations need not be simply related to the actual geometry of spacetime. One specific consequence of this is a decoupling of the geometrical spatial curvature term in the metric from the dynamical spatial curvature in the Friedmann equation. Here we investigate the consequences of this decoupling by fitting to a combination of Hubble Space Telescope (HST), CMB, type Ia supernovae (SNIa), and baryon acoustic oscillation (BAO) data sets. We find that only the geometrical spatial curvature is tightly constrained and that our ability to constrain dark energy dynamics will be severely impaired until we gain a thorough understanding of the averaging problem in cosmology.

30 citations

Journal ArticleDOI
TL;DR: Cactus as mentioned in this paper is a 3D multi-purpose parallel code for general relativistic astrophysics, which can be used to simulate colliding black holes and neutron stars, as well as accelerate the complete set of Einstein's equations for the first time.

30 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20232
20226
20191
20185
201734
201662