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Mathematics of general relativity

About: Mathematics of general relativity is a research topic. Over the lifetime, 2100 publications have been published within this topic receiving 68381 citations.


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Book
01 Jan 2008
TL;DR: The 3+1 formalism has been studied extensively in the literature as discussed by the authors, where the authors present a brief review of general Relativity and its applications in 3+ 1 languages.
Abstract: 1. Brief Review of General Relativity 2. The 3+1 Formalism 3. Initial Data 4. Gauge Conditions 5. Hyperbolic Reductions of the Field Equations 6. Evolving Black Hole Spacetimes 7. Relativistic Hydrodynamics 8. Gravitational Wave Extraction 9. Numerical Methods 10. Examples of Numerical Spacetimes A. Total Mass and Momentum in General Relativity B. Spacetime Christoffel Symbols in 3+1 Language C. BSSNOK with Natural Conformal Rescaling D. Spin-weighted Spherical Harmonics References Index

564 citations

Journal ArticleDOI
TL;DR: In this article, a calculus for general relativity is developed in which the basic role of tensors is taken over by spinors, and the Riemann-Christoffel tensor is written in a spinor form according to a scheme of Witten.

559 citations

Journal ArticleDOI
TL;DR: In this article, a general theory of complex V4 spaces of this type is outlined and examples of nontrivial solutions of all degenerate algebraic types are provided, where Γ = 0 and therefore a fortiori equations Gab = 0 are fulfilled.
Abstract: Complex V4’s are investigated where ΓȦḂ =0 and therefore a fortiori equations Gab=0 are fulfilled. A general theory of spaces of this type is outlined and examples of nontrivial solutions of all degenerate algebraic types are provided.

498 citations

Book
01 Jan 1950
TL;DR: In this article, the Unconnected Manifold and the affinely connected manifold are discussed, and the meaning of the metric according to the special theory of relativity is discussed.
Abstract: Introduction Part I. The Unconnected Manifold: 1. Invariance 2. Integrals Part II. Affinely Connected Manifold: 3. Invariant derivatives 4. Some relations between ordinary and invariant derivatives 5. The notion of parallel transfer 6. The curvature tensor 7. The geodesics of an affine connexion 8. The general geometrical hypothesis about gravitation Part III. Metrically Connected Manifold: 9. Metrical affinities 10. The meaning of the metric according to the special theory of relativity 11. Conservation laws and variational principles 12. Generalizations of Einstein's theory.

478 citations

Journal ArticleDOI
TL;DR: A review of the teleparallel equivalent of general relativity is presented in this paper, where the equivalence with the standard formulation in terms of the metric and curvature tensors takes place at the level of field equations.
Abstract: A review of the teleparallel equivalent of general relativity is presented. It is emphasized that general relativity may be formulated in terms of the tetrad fields and of the torsion tensor, and that this geometrical formulation leads to alternative insights into the theory. The equivalence with the standard formulation in terms of the metric and curvature tensors takes place at the level of field equations. The review starts with a brief account of the history of teleparallel theories of gravity. Then the ordinary interpretation of the tetrad fields as reference frames adapted to arbitrary observers in space–time is discussed, and the tensor of inertial accelerations on frames is obtained. It is shown that the Lagrangian and Hamiltonian field equations allow us to define the energy, momentum and angular momentum of the gravitational field, as surface integrals of the field quantities. In the phase space of the theory, these quantities satisfy the algebra of the Poincare group.

468 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20231
202216
20202
20192
20183
201734