Deviation operator and deviation equations over spaces with affine connections and metrics

Manoff, S.

doi:10.1016/s0393-0440(01)00019-5

Cited by 10 publications

(6 citation statements)

References 33 publications

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“…In contrast to a Riemannian spacetime a Riemann-Cartan spacetime is endowed with an asymmetric connection Γ ab c , and there will be differences when it comes to the basic properties of a world function σ based on autoparallels. We base our presentation on [56], other relevant references which contain some results in a Riemann-Cartan context are [61,62,63,64,65,66,67,68].…”

Section: World Function In Riemann-cartan Spacetimementioning

confidence: 99%

Measuring the Gravitational Field in General Relativity: From Deviation Equations and the Gravitational Compass to Relativistic Clock Gradiometry

Obukhov

Puetzfeld

2019

Fundamental Theories of Physics

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How does one measure the gravitational field? We give explicit answers to this fundamental question and show how all components of the curvature tensor, which represents the gravitational field in Einstein's theory of General Relativity, can be obtained by means of two different methods. The first method relies on the measuring the accelerations of a suitably prepared set of test bodies relative to the observer. The second methods utilizes a set of suitably prepared clocks. The methods discussed here form the basis of relativistic (clock) gradiometry and are of direct operational relevance for applications in geodesy. *

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Section: World Function In Riemann-cartan Spacetimementioning

confidence: 99%

Measuring the Gravitational Field in General Relativity: From Deviation Equations and the Gravitational Compass to Relativistic Clock Gradiometry

Obukhov

Puetzfeld

2019

Fundamental Theories of Physics

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“…In this section we work out the basic properties of a world function σ based on autoparallels in a Riemann-Cartan spacetime, which, in contrast to a Riemannian spacetime, is endowed with an asymmetric connection Γ ab c . Relevant references that contain some results in a Riemann-Cartan context are [37][38][39][40][41][42][43][44].…”

Section: World Function In Riemann-cartan Spacetimementioning

confidence: 99%

Deviation equation in Riemann-Cartan spacetime

Puetzfeld

Obukhov

2018

Phys. Rev. D

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“…Generalizations of equation (1) to admit arbitrary relative velocities were obtained and applied in the works [119][120][121][122][123][124][126][127][128]. Further extensions, higher-order corrections to the geodesic deviation equation and their specific applications can be found in [130][131][132][133][134][135] (for reviews and other references see [118,128,131,135]). Our aim, however, in this paper is to investigate local relative motion of nearby free test particles which are initially at rest with respect to each other.…”

Section: Equation Of Geodesic Deviationmentioning

confidence: 99%

“…Let us also mention that generalizations of the equation of geodesic deviation to admit arbitrary relative velocities of the particles were obtained in the works [119][120][121][122][123][124][125][126][127][128]. Further extensions, higher-order corrections to the geodesic devia-tion equation, their particular applications and references can be found in the recent papers [128][129][130][131][132][133][134][135] and in the monograph [118].…”

Section: Introductionmentioning

confidence: 99%

Interpreting spacetimes of any dimension using geodesic deviation

Podolský

Švarc

2012

Phys. Rev. D

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We present a general method which can be used for geometrical and physical interpretation of an arbitrary spacetime in four or any higher number of dimensions. It is based on the systematic analysis of relative motion of free test particles. We demonstrate that local effect of the gravitational field on particles, as described by equation of geodesic deviation with respect to a natural orthonormal frame, can always be decomposed into a canonical set of transverse, longitudinal and Newton-Coulombtype components, isotropic influence of a cosmological constant, and contributions arising from specific matter content of the universe. In particular, exact gravitational waves in Einstein's theory always exhibit themselves via purely transverse effects with D(D − 3)/2 independent polarization states. To illustrate the utility of this approach we study the family of pp-wave spacetimes in higher dimensions and discuss specific measurable effects on a detector located in four spacetime dimensions. For example, the corresponding deformations caused by a generic higher-dimensional gravitational waves observed in such physical subspace, need not be tracefree.

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Deviation operator and deviation equations over spaces with affine connections and metrics

Cited by 10 publications

References 33 publications

Measuring the Gravitational Field in General Relativity: From Deviation Equations and the Gravitational Compass to Relativistic Clock Gradiometry

Measuring the Gravitational Field in General Relativity: From Deviation Equations and the Gravitational Compass to Relativistic Clock Gradiometry

Deviation equation in Riemann-Cartan spacetime

Interpreting spacetimes of any dimension using geodesic deviation

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