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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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Journal ArticleDOI
01 Apr 2010
TL;DR: In this article, the phenomenology of models possessing a non-minimal coupling between matter and geometry is discussed, with a particular focus on the possibility of describing the flattening of the galactic rotation curves as a dynamically generated effect derived from this modification to General Relativity.
Abstract: In this work the phenomenology of models possessing a non-minimal coupling between matter and geometry is discussed, with a particular focus on the possibility of describing the flattening of the galactic rotation curves as a dynamically generated effect derived from this modification to General Relativity. Two possibilities are discussed: firstly, that the observed discrepancy between the measured rotation velocity and the classical prediction is due to a deviation from geodesic motion, due to a non-(covariant) conservation of the energy-momentum tensor; secondly, that even if the principle of energy conservation holds, the dynamical effects arising due to the non-trivial terms in the Einstein equations of motion can give rise to an extra density contribution that may be interpreted as dark matter. In this work, The mechanism of the latter alternative is detailed; a numerical session ascertaining the order of magnitude of the relevant parameters is undertaken in another contribution to this volume, with possible cosmological implications discussed.

15 citations

Journal ArticleDOI
TL;DR: In this article, the authors discuss the relation between Relativity before 1905 and special Relativity-Kinematics and its kinetics, including Arbitrary Frames, Surfaces and Curvature, and Intrinsic Geometry.
Abstract: 1 Relativity Before 1905.- 2 Special Relativity-Kinematics.- 3 Special Relativity-Kinetics.- 4 Arbitrary Frames.- 5 Surfaces and Curvature.- 6 Intrinsic Geometry.- 7 General Relativity.- 8 Consequences.

15 citations

Journal ArticleDOI
TL;DR: In this article, an approximate coordinate transformation to an accelerated frame was proposed, which turns out to be closely related to Rindler coordinates, widely used in modern general relativity, leading him directly to interpret gravitation in terms of spacetime curvature.
Abstract: On his way to general relativity, Einstein used the equivalence principle to formulate a theory of the static gravitational field. In this context he introduced an approximate coordinate transformation to an accelerated frame which turns out to be closely related to Rindler coordinates, widely used in modern general relativity. This work, published in the Annalen, led him directly to interpret gravitation in terms of spacetime curvature.

15 citations

Journal ArticleDOI
TL;DR: In this article, a tensor model around its classical background of two-, three-and four-dimensional fuzzy flat tori is studied and it is shown that the properties of low-lying low-momentum modes are in clear agreement with general relativity.
Abstract: Tensor models can be regarded as theories of dynamical fuzzy spaces, and provide background independent theories of space. Their classical solutions correspond to classical background spaces, and the small fluctuations around them can be regarded as fluctuations of fields on them. In this paper, I numerically study a tensor model around its classical backgrounds of two-, three- and four-dimensional fuzzy flat tori and show that the properties of low-lying low-momentum modes are in clear agreement with general relativity. Numerical analysis also suggests that the lowest-order effective action is composed of curvature square terms, which is consistent with general relativity in view of the form of the considered action of the tensor model.

15 citations

Journal ArticleDOI
TL;DR: In this article, an interior solution in higher dimensions which corresponds to the interior Schwarzschild solution in four-dimensional general relativity was presented, and the interior solution was shown to be the same as in four dimensions.

15 citations


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