On the Applicability of the Geodesic Deviation Equation in General Relativity

Philipp, Dennis; Puetzfeld, Dirk; Lämmerzahl, Cláus

doi:10.1007/978-3-030-11500-5_13

Cited by 7 publications

(8 citation statements)

References 24 publications

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“…This characteristic behaviour is similar to that possessed by Re( α(t, 1, z) ). It suggests that "tidal forces" (responsible for the geodesic deviation of neighbouring geodesics [20,21,22]) are concentrated in spacetime regions where components of the Riemann tensor of g (0) have pulse-like behaviour in domains similar to those possessed by R g (0) (t, ρ, z). Explicit formulae for R g (0) (t, ρ, z) and H(t, ρ, φ, z) are not particularly illuminating 6 .…”

Section: Gravitational Pulses In Vacuamentioning

confidence: 99%

Scalar Pre-potentials for Spinor and Tensor Fields on Spacetime

Tucker,

Walton

2021

Preprint

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We review a technique for solving a class of classical linear partial differential systems of relevance to physics in Minkowski spacetime. All the equations are amenable to analysis in terms of complex solutions in the kernel of the scalar Laplacian and a complexified Hertz potential. The complexification prescription ensures the existence of regular physical solutions with chirality and propagating, non-singular, pulselike characteristics that are bounded in all three spatial dimensions. The technique is applied to the source-free Maxwell, Bopp-Landé-Podolsky and linearised Einstein field systems, and particular solutions are used for constructing classical models describing single-cycle laser pulses and a mechanism is discussed for initiating astrophysical jets. Our article concludes with a brief introduction to spacetime Clifford algebra ideals that we use to represent spinor fields. We employ these to demonstrate how the same technique used for tensor fields enables one to construct new propagating, chiral, non-singular, pulse-like spinor solutions to the massless Dirac equation in Minkowski spacetime.

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Section: Gravitational Pulses In Vacuamentioning

confidence: 99%

Scalar Pre-potentials for Spinor and Tensor Fields on Spacetime

Tucker,

Walton

2021

Preprint

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“…Thus with sufficient knowledge of families of geodesics in some domain of space-time one can reconstruct the Riemann tensor in the whole domain in terms of a Taylor series from the geodesic deviations w.r.t. a given geodesic [10,11,12]. The procedure described here has been worked out for Schwarzschild space-time up to and including the second-order deviations [6,13,14].…”

Section: Geodesic Deviationsmentioning

confidence: 99%

World-Line Perturbation Theory

Holten

2019

Fundamental Theories of Physics

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The motion of a compact body in space and time is commonly described by the world line of a point representing the instantaneous position of the body. In General Relativity such a world-line formalism is not quite straightforward because of the strict impossibility to accommodate point masses and rigid bodies. In many situations of practical interest it can still be made to work using an effective hamiltonian or energy-momentum tensor for a finite number of collective degrees of freedom of the compact object. Even so exact solutions of the equations of motion are often not available. In such cases families of world lines of compact bodies in curved space-times can be constructed by a perturbative procedure based on generalized geodesic deviation equations. Examples for simple test masses and for spinning test bodies are presented. *

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“…This characteristic behaviour is similar to that possessed by Re( α (T, 1, Z) ). It suggests that "tidal forces" (responsible for the geodesic deviation of neighbouring geodesics [20,21,22]) are concentrated in spacetime regions where components of the Riemann tensor of g 0 have pulse-like behaviour in domains similar to those possessed by R g 0 (T, R, Z).…”

Section: Gravitational Pulses In Vacuamentioning

confidence: 99%

Chirality in gravitational and electromagnetic interactions with matter

Tucker

Walton

2018

Int. J. Geom. Methods Mod. Phys.

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It has been suggested that single and double jets observed emanating from certain astrophysical objects may have a purely gravitational origin. We discuss new classes of pulsed gravitational wave solutions to the equation for perturbations of Ricci-flat spacetimes around Minkowski metrics, as models for the genesis of such phenomena. We discuss how these solutions are motivated by the analytic structure of spatially compact finite energy pulse solutions of the source-free Maxwell equations generated from complex chiral eigenmodes of a chirality operator. Complex gravitational pulse solutions to the linearised source-free Einstein equations are classified in terms of their chirality and generate a family of non-stationary real spacetime metrics. Particular members of these families are used as backgrounds in analysing time-like solutions to the geodesic equation for test particles. They are found numerically to exhibit both single and double jet-like features with dimensionless aspect ratios suggesting that it may be profitable to include such backgrounds in simulations of astrophysical jet dynamics from rotating accretion discs involving electromagnetic fields.

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On the Applicability of the Geodesic Deviation Equation in General Relativity

Cited by 7 publications

References 24 publications

Scalar Pre-potentials for Spinor and Tensor Fields on Spacetime

Scalar Pre-potentials for Spinor and Tensor Fields on Spacetime

World-Line Perturbation Theory

Chirality in gravitational and electromagnetic interactions with matter

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