Geodesic deviation in Kaluza-Klein theories

Kerner, Richard; Martin, Jerome; Mignemi, Salvatore; Holten, Jan-Willem van

doi:10.1103/physrevd.63.027502

Cited by 32 publications

(43 citation statements)

References 7 publications

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“…This approach, has been already used for studying the Lorentz force equation in General Relativity (see for instance [4]) but a result, a la Avez and Seifert, for the Lorentz force equation was still lacking.…”

Section: Introductionmentioning

confidence: 99%

Solutions to the Lorentz force equation with fixed charge-to-mass ratio in globally hyperbolic space–times

Caponio

Minguzzi

2004

Journal of Geometry and Physics

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Abstract. We extend the classical Avez-Seifert theorem to trajectories of charged test particles with fixed charge-to-mass ratio. In particular, given two events x 0 and x 1 , with x 1 in the chronological future of x 0 , we find an interval I =] − R, R[ such that for any q/m ∈ I there is a timelike connecting solution of the Lorentz force equation. Moreover, under the assumption that there is no null geodesic connecting x 0 and x 1 , we prove that to any value of |q/m| there correspond at least two connecting timelike solutions which coincide only if they are geodesics.

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Section: Introductionmentioning

confidence: 99%

Solutions to the Lorentz force equation with fixed charge-to-mass ratio in globally hyperbolic space–times

Caponio

Minguzzi

2004

Journal of Geometry and Physics

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“…Geodesics deviations in vacuum space-times, namely, Schwarzschild and Reissner-Nordström space-times, are rigorously studied in [11]- [17]. Some studies on geodesic deviation can be found in [18]- [20]. Ghosh and Kar [21] investigated geodesic motion and geodesic deviation in warped space-times with a a time dependent extra dimension.…”

Section: Introductionmentioning

confidence: 99%

Geodesics and geodesic deviation in static charged black holes

Gad

2010

Astrophys Space Sci

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The radial motion along null geodesics in static charged black hole space-times, in particular, the Reissner-Nordström and stringy charged black holes are studied. We analyzed the properties of the effective potential. The circular photon orbits in these space-times are investigated. We found that the radius of circular photon orbits in both charged black holes are different and differ from that given in Schwarzschild space-time. We studied the physical effects of the gravitational field between two test particles in stringy charged black hole and compared the results with that given in Schwarzschild and Reissner-Nordström black holes.

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“…An approach conceived to study directly the physical question (Q) started in [17], [29], where the authors considered the solutions to the LFE as projections of suitable lightlike geodesics for a Kaluza-Klein metric. It is well known the relation between the LFE and the projections of timelike geodesics for a higher dimensional Kaluza-Klein spacetime [21][22][23][24]27,28]. However, it proved more useful for question (Q) to consider the solutions of the LFE as projections of lightlike geodesics in a Kaluza-Klein spacetime with a scale factor (for the additional dimension) proportional to the charge-to-mass ratio.…”

Section: Known Results On (Q)mentioning

confidence: 99%

Connecting Solutions of the Lorentz Force Equation do Exist

Minguzzi

Sánchez

2006

Commun. Math. Phys.

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Recent results on the maximization of the charged-particle action I x0,x1 in a globally hyperbolic spacetime are discussed and generalized. We focus on the maximization of I x0,x1 over a given causal homotopy class C of curves connecting two causally related events x 0 ≤ x 1 . Action I x0,x1 is proved to admit a maximum on C, and also one in the adherence of each timelike homotopy class C. Moreover, the maximum σ 0 on C is timelike if C contains a timelike curve (and the degree of differentiability of all the elements is at least C 2 ). In particular, this last result yields a complete Avez-Seifert type solution to the problem of connectedness through trajectories of charged particles in a globally hyperbolic spacetime endowed with an exact electromagnetic field: fixed any charge-to-mass ratio q/m, any two chronologically related events x 0 ≪ x 1 can be connected by means of a timelike solution of the Lorentz force equation (LFE) corresponding to q/m. The accuracy of the approach is stressed by many examples, including an explicit counterexample (valid for all q/m) in the nonexact case.As a relevant previous step, new properties of the causal path space, causal homotopy classes and cut points on lightlike geodesics are studied.

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Geodesic deviation in Kaluza-Klein theories

Cited by 32 publications

References 7 publications

Solutions to the Lorentz force equation with fixed charge-to-mass ratio in globally hyperbolic space–times

Solutions to the Lorentz force equation with fixed charge-to-mass ratio in globally hyperbolic space–times

Geodesics and geodesic deviation in static charged black holes

Connecting Solutions of the Lorentz Force Equation do Exist

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