Deviation equation in Riemann-Cartan spacetime

Puetzfeld, Dirk; Obukhov, Yuri N.

doi:10.1103/physrevd.97.104069

Cited by 8 publications

(13 citation statements)

References 43 publications

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“…However, it means that there is no coordinate grid associated with our (l, η) frame, as one would expect for a smooth congruence, and this makes it less useful a priori. We leave further considerations on the geometric meaning of (58) for future work, and keep (53) in the following, which seems to us also supported by the coordinate analysis performed in [9,11].…”

Section: Torsion-full Null Geodesic Congruencesmentioning

confidence: 70%

“…However this equation should not be taken as the Raychaudhuri equation in the presence of torsion, because θ does not have the geometric interpretation of the expansion of the congruence. This was discussed in [9] (see also [10,11]), and starting from the observation that the true displacement tensor is (57), the expansion was identified with θ ′ . We have confirmed this by looking at the propagation equations (64).…”

Section: Raychaudhuri Equation With Torsionmentioning

confidence: 99%

“…In spite of these limitations, the geodesic deviation and associated Raychaudhuri equations with torsion have been studied in the literature, often motivated by applications to modified theories of gravity, see e.g. [1,8] for early work and more recently [9,10,11,12]. In this brief note we restrict attention to null geodesic congruences (NGCs), rederive results of [9] and extend the analysis to include the null Raychaudhuri and the rest of Sachs' optical equations with torsion.…”

Section: Introductionmentioning

confidence: 99%

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Raychaudhuri and optical equations for null geodesic congruences with torsion

Speziale

2018

Phys. Rev. D

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We study null geodesic congruences (NGCs) in the presence of spacetime torsion, recovering and extending results in the literature. Only the highest spin irreducible component of torsion gives a proper acceleration with respect to metric NGCs, but at the same time obstructs abreastness of the geodesics. This means that it is necessary to follow the evolution of the drift term in the optical equations, and not just shear, twist and expansion. We show how the optical equations depend on the non-Riemannian components of the curvature, and how they reduce to the metric ones when the highest spin component of torsion vanishes.

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Section: Torsion-full Null Geodesic Congruencesmentioning

confidence: 70%

Section: Raychaudhuri Equation With Torsionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Raychaudhuri and optical equations for null geodesic congruences with torsion

Speziale

2018

Phys. Rev. D

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“…For recent work on general relativistic tidal effects in other contexts, see, for example, Refs. [16][17][18][19][20][21][22] and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

Critical Tidal Currents in General Relativity

Mashhoon

2020

Universe

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Relativistic tidal equations are formulated with respect to the rest frame of a central gravitational source and their solutions are studied. The existence of certain relativistic critical tidal currents are thereby elucidated. Specifically, observers that are spatially at rest in the exterior Kerr spacetime are considered in detail; in effect, these fiducial observers define the rest frame of the Kerr source. The general tidal equations for the free motion of test particles are worked out with respect to the Kerr background. The analytic solutions of these equations are investigated and the existence of a tidal acceleration mechanism is emphasized.

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“…Therefore, in view of possible tests of gravitational theories by means of structured test bodies, a further extension of the deviation equation to post-Riemannian geometries is needed. In the following we present a generalized deviation equation in a Riemann-Cartan background, allowing for spacetimes endowed with torsion, the presentation is based on [56]. This equation describes the dynamics of the connecting vector which links events on two general (adjacent) world lines.…”

Section: Outlook: Operational Determination Of the Gravitational Fielmentioning

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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Deviation equation in Riemann-Cartan spacetime

Cited by 8 publications

References 43 publications

Raychaudhuri and optical equations for null geodesic congruences with torsion

Raychaudhuri and optical equations for null geodesic congruences with torsion

Critical Tidal Currents in General Relativity

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

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