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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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Book
01 Jan 1982
TL;DR: In this paper, a spinor formulation of gravitation and a classification of the gravitational and gauge fields is proposed. But the classification is based on the spinor model and not on the geodesic geometry of curved space-time.
Abstract: The gravitational field the geometry of curved space-time the Einstein field equations gravitational fields of elementary mass systems properties of the gravitational field equations of motion in general relativity axisymmetric solutions of the Einstein field equations spinor formulation of gravitation and gauge fields classification of the gravitational and gauge fields gauge theory of gravitation and other fields extended bodies in general relativity.

362 citations

Book
29 Apr 2004
TL;DR: In this article, the Lorentz group is used to construct curvature structures in space-time holonomy curvature collineations and sectional curvature structure in general relativity affine symmetries.
Abstract: Introduction topological spaces groups and linear algebra manifold theory transformation groups the Lorentz group general relativity theory space-time holonomy curvature structure in general relativity affine symmetries in space-time conformal symmetries in space-time curvature collineations sectional curvature structure.

358 citations

Journal ArticleDOI
TL;DR: The present status of the quasi-local mass, energy-Momentum and angular-momentum constructions in general relativity is reviewed.
Abstract: The present status of the quasi-local mass, energy-momentum and angular-momentum constructions in general relativity is reviewed. First, the general ideas, concepts, and strategies, as well as the necessary tools to construct and analyze the quasi-local quantities, are recalled. Then, the various specific constructions and their properties (both successes and deficiencies are discussed. Finally, some of the (actual and potential) applications of the quasi-local concepts and specific constructions are briefly mentioned.

354 citations

Book
01 Jan 1982
TL;DR: The foundations of special relativity can be found in this paper, where the Minkowski map of spacetime rules for the manipulation of 4-tensors 4-velocity and 4-acceleration wave motion.
Abstract: Part 1 The foundations of special relativity: schematic account of the Michelson - Morley experiment inertial frames in special relativity Einstein's two axioms for special relativity coordinates - the relativity of time derivation of the Lorentz transformation properties of the Lorentz transformation. Part 2 Relativistic kinematics: length contraction the length contraction paradox time dilation the twin paradox velocity transformation. Part 3 Relativistic optics: the drag effect the Doppler effect aberration and the visual appearance of moving objects. Part 4 Spacetime: spacetime and 4-tensors the Minkowski map of spacetime rules for the manipulation of 4-tensors 4-velocity and 4-acceleration wave motion. Part 5 Relativistic particle mechanics: the conservation of 4-momentum the equivalence of mass and energy some 4-momentum identities relativistic billiards the centre of momentum frame threshold energies De Broglie waves photons the angular momentum 4-tensor 3-force and 4-force relativistic analytic mechanics. Part 6 Relativity and electromagnetism: the formal structure of Maxwell's theory transformation of "e" and "b" - the deal field potential and field of an arbitrarily moving charge field of a uniformly moving charge the electromagnetic energy tensor electromagnetic waves. Part 7 Relativistic mechanics of continua: preliminaries external and internal forces the augmented momentum and mass densities the equations of continuity and of motion the mechanical energy tensor perfect fluids and incoherent fluids integral conservation laws. Appendix - tensors for special relativity.

346 citations

Book
01 Jan 2005
TL;DR: In this article, the authors discuss the history of the Lorentz transformations in special relativity and quantum theory, including the trailblazers of Albert Keinstein and his followers.
Abstract: 1 Overview 2 The physics of coordinate transformations 3 The relativity principle and the fable of Albert Keinstein 4 The trailblazers 5 Einstein's principle-theory route to the Lorentz transformations 6 Variations on the Einstein theme 7 Unconventional voices on special relativity 8 What is special relativity? 9 The view from general relativity APPENDICES A Einstein on general covariance B Special relativity and quantum theory

345 citations


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