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Geodesic deviation

About: Geodesic deviation is a research topic. Over the lifetime, 457 publications have been published within this topic receiving 15609 citations.


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01 Jan 1984

8,137 citations

Book
31 Mar 2004
TL;DR: In this article, the authors proposed a generalization of the Brans-Dicke cosmology in the Jordan frame to general relativity, which is the limit of general relativity.
Abstract: 1. Scalar-Tensor Gravity.- 1 Introduction.- 2 Brans-Dicke theory.- 3 Brans-Dicke cosmology in the Jordan frame.- 4 The limit to general relativity.- 5 Relation to Kaluza-Klein theory.- 6 Brans-Dicke theory from Lyra's geometry.- 7 Scalar-tensor theories.- 7.1 Effective Lagrangians and Hamiltonians.- 8 Motivations for scalar-tensor theories.- 9 Induced gravity.- 10 Generalized scalar-tensor theories.- 11 Conformal transformation techniques.- 11.1 Conformal transformations.- 11.2 Brans-Dicke theory.- 11.3 Kaluza-Klein cosmology.- 11.4 Scalar-tensor theories.- 11.5 Generalized scalar-tensor theories.- 12 Singularities of the gravitational coupling.- 2. Effective Energy-Momentum Tensors and Conformal Frames.- 1 The issue of the conformal frame.- 1.1 The first viewpoint.- 1.2 The second viewpoint.- 1.3 The third viewpoint.- 1.4 Other viewpoints.- 1.5 Einstein frame or Jordan frame?.- 1.6 Energy conditions in relativistic theories.- 1.7 Singularity theorems and energy conditions.- 2 Effective energy-momentum tensors.- 2.1 Time-dependence of the gravitational coupling.- 2.2 Conservation equations for the various Tab(J) [oo].- 3. Gravitational Waves.- 1 Introduction.- 2 Einstein frame scalar-tensor waves.- 2.1 Gravitational waves in the Einstein frame.- 2.2 Corrections to the geodesic deviation equation.- 3 Gravitational lensing by scalar-tensor gravitational waves.- 3.1 Jordan frame analysis.- 3.2 Einstein frame analysis.- 3.3 Propagation of light through a gravitational wave background.- 4. Exact Solutions of Scalar-Tensor Cosmology.- 1 Introduction.- 2 Exact solutions of Brans-Dicke cosmology.- 2.1 K = 0 FLRW solutions.- 2.1.1 The O'Hanlon and Tupper solution.- 2.1.2 The Brans-Dicke dust solution.- 2.1.3 The Nariai solution.- 2.1.4 Other solutions with cosmological constant.- 2.1.5 Generalizing Nariai's solution.- 2.1.6 Phase space analysis for K = 0 and V(o) = 0.- 2.1.7 Phase plane analysis for K = 0 and V(o) = Ao.- 2.2 K = +-1 solutions and phase space for V = 0.- 2.3 Phase space for any K and V = m2o2/2.- 2.3.1 The Dehnen-Obregon solution.- 2.4 Bianchi models.- 2.4.1 Bianchi V universes.- 3 Exact solutions of scalar-tensor theories.- 5. The Early Universe.- 1 Introduction.- 2 Extended inflation.- 2.1 The original extended inflationary scenario.- 2.2 Alternatives.- 3 Hyperextended inflation.- 4 Real inflation?.- 5 Constraints from primordial nucleosynthesis.- 6. Perturbations.- 1 Introduction.- 2 Scalar perturbations.- 3 Tensor perturbations.- 7. Nonminimal Coupling.- 1 Introduction.- 1.1 Generalized inflation.- 1.2 Motivations for nonminimal coupling.- 1.3 Which value of.- 2 Effective energy-momentum tensors.- 2.1 Approach a la Callan-Coleman-Jackiw.- 2.2 Effective coupling.- 2.3 A mixed approach.- 2.4 Discussion.- 2.5 Energy conditions in FLRW cosmology.- 2.6 Nonminimal coupling and gravitational waves.- 3 Conformal transformations.- 4 Inflation and ? 0: the unperturbed universe.- 4.1 Necessary conditions for generalized inflation.- 4.1.1 Specific potentials.- 4.2 The effective equation of state with nonminimal coupling.- 4.3 Critical values of the scalar field.- 5 The slow-roll regime of generalized inflation.- 5.1 Derivation of the stability conditions.- 5.2 Slow-roll parameters.- 6 Inflation and ? 0: perturbations.- 6.1 Density perturbations.- 6.2 Tensor perturbations.- 7 Conclusion.- 8. The Present Universe.- 1 Present acceleration of the universe and quintessence.- 1.1 Coupled quintessence.- 1.2 Multiple field quintessence.- 1.3 Falsifying quintessence models.- 2 Quintessence with nonminimal coupling.- 2.1 Models using the Ratra-Peebles potential.- 2.2 Necessary conditions for accelerated expansion.- 2.3 Doppler peaks with nonminimal coupling.- 3 Superquintessence.- 3.1 An exact superaccelerating solution.- 3.2 Big Smash singularities.- 4 Quintessence in scalar-tensor gravity.- 5 Conclusion.- References.

711 citations

Journal ArticleDOI
TL;DR: In this paper, a covariant formulation of the outgoing radiation condition for gravitational fields is proposed, based on a detailed examination of the geometry of null lines and of the algebraic and differential properties of the Riemann tensor.
Abstract: A covariant formulation of the outgoing radiation condition for gravitational fields is proposed. The condition is based on a detailed examination of the geometry of null lines and of the algebraic and differential properties of the Riemann tensor. It relates the absence of incoming radiation, in a gravitational field with bounded sources and Euclidean topology, to the asymptotic behaviour of the Riemann tensor. Fields that are algebraically special in the Petrov classification are highly special examples of fields obeying the suggested condition.

586 citations

Journal ArticleDOI
TL;DR: Gravitational lensing has developed into one of the most powerful tools for the analysis of the dark universe as mentioned in this paper, and its main current applications and representative results achieved so far.
Abstract: Gravitational lensing has developed into one of the most powerful tools for the analysis of the dark universe. This review summarises the theory of gravitational lensing, its main current applications and representative results achieved so far. It has two parts. In the first, starting from the equation of geodesic deviation, the equations of thin and extended gravitational lensing are derived. In the second, gravitational lensing by stars and planets, galaxies, galaxy clusters and large-scale structures is discussed and summarised.

404 citations

Journal ArticleDOI
TL;DR: In this article, a discussion of the use of the modern, coordinate-free concept of a vector and of computations which are simplified by introducing a vector instead of its components is presented.
Abstract: Fermi coordinates, where the metric is rectangular and has vanishing first derivatives at each point of a curve, are constructed in a particular way about a geodesic. This determines an expansion of the metric in powers of proper distance normal to the geodesic, of which the second‐order terms are explicitly computed here in terms of the curvature tensor at the corresponding point on the base geodesic. These terms determine the lowest‐order effects of a gravitational field which can be measured locally by a freely falling observer. An example is provided in the Schwarzschild metric. This discussion of Fermi Normal Coordinate provides numerous examples of the use of the modern, coordinate‐free concept of a vector and of computations which are simplified by introducing a vector instead of its components. The ideas of contravariant vector and Lie Bracket, as well as the equation of geodesic deviation, are reviewed before being applied.

330 citations

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202126
202025
201924
201819
201715
201624