Generalized geodesic deviations: a Lagrangean approach

Kerner, Richard

doi:10.4064/bc59-0-9

Cited by 3 publications

(2 citation statements)

References 18 publications

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“…It is also stated that the difference is due to the fact that Weber first linearizes the equation of motion, and that Weber's Hamiltonian is not valid if the test particle is charged. 16 Detailed treatments of the Lagrangian and Hamiltonian formulation of geodesic deviation can be found in [80,81,82]. 17 It is argued in [83] that Fermi normal coordinates are appropriate for a problem involving energy levels, in contrast to Riemann normal coordinates.…”

Section: Alternative Hamiltonians and Methods Of Coupling Gravity To ...mentioning

confidence: 99%

Superconductor Meissner Effects for Gravito-Electromagnetic Fields in Harmonic Coordinates Due to Non-Relativistic Gravitational Sources

Inan

2022

Front. Phys.

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There is much discrepancy in the literature concerning the possibility of a superconductor expelling gravito-electromagnetic fields just as it expels electromagnetic fields in the Meissner effect. Contradicting results are found in at least 18 papers written collectively by more than 20 authors and published over the course of more than 55 years (from 1966 to the present year of 2022). The primary purpose of this paper is to carefully explain the reason for the discrepancies, and provide a single conclusive treatment which may bring coherence to the subject. The analysis begins with a covariant Lagrangian for spinless charged particles (Cooper pairs) in the presence of electromagnetic fields in curved space-time. It is known that such a Lagrangian can lead to a vanishing Hamiltonian. Alternatively, it is shown that using a “space + time” Lagrangian leads to an associated Hamiltonian with a canonical momentum and minimal coupling rule. Discrepancies between Hamiltonians obtained by various authors are resolved. The canonical momentum leads to a modified form of the London equations and London gauge that includes the effects of gravity. A key result is that the gravito-magnetic field is expelled from a superconductor with a penetration depth on the order of the London penetration depth only when an appropriate magnetic field is also present. The gravitational flux quantum (fluxoid) in the body of a superconductor, and the quantized supercurrent in a superconducting ring, are also derived. Lastly, the case of a superconducting ring in the presence of a charged rotating mass cylinder is used as an example of applying the formalism developed.

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Section: Alternative Hamiltonians and Methods Of Coupling Gravity To ...mentioning

confidence: 99%

Superconductor Meissner Effects for Gravito-Electromagnetic Fields in Harmonic Coordinates Due to Non-Relativistic Gravitational Sources

Inan

2022

Front. Phys.

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“…In [28] a method is presented that generalizes the Hamilton-Jacobi equation, allowing to obtain at the same time solutions of the geodesic and the geodesic deviation equations. A Lagrangian formulation of the geodesic deviation equations, including an electromagnetic field and spin, and a treatment of higher order deviation equations can be found in [7,13,29], and is obtained by an expansion of that of geodesic motion. Given this natural connection, it is reasonable to expect that symmetries of dynamics of the geodesic motion, when present, descend to symmetries of the Jacobi equation.…”

Section: Introductionmentioning

confidence: 99%

On integrability of the geodesic deviation equation

et al. 2018

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The Jacobi equation for geodesic deviation describes finite size effects due to the gravitational tidal forces. In this paper we show how one can integrate the Jacobi equation in any spacetime admitting completely integrable geodesics. Namely, by linearizing the geodesic equation and its conserved charges, we arrive at the invariant Wronskians for the Jacobi system that are linear in the 'deviation momenta' and thus yield a system of first-order differential equations that can be integrated. The procedure is illustrated on an example of a rotating black hole spacetime described by the Kerr geometry and its higher-dimensional generalizations. A number of related topics, including the phase space formulation of the theory and the derivation of the covariant Hamiltonian for the Jacobi system are also discussed.1 The convention we use in this work for the commutation of covariant derivatives, when acting for example on a vector V a , is

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Higher-order geodesic deviation for charged particles and resonance induced by gravitational waves

Heydari-Fard

Hasani

2018

Int. J. Mod. Phys. D

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We generalize the higher-order geodesic deviation for the structure-less test particles to the higher-order geodesic deviation equations of the charged particles [R. Kerner, J. W. van Holten and R. Colistete Jr., Class. Quantum Grav. 18 (2001) 4725]. By solving these equations for charged particles moving in a constant magnetic field in the spacetime of a gravitational wave, we show for both cases when the gravitational wave is parallel and perpendicular to the constant magnetic field, a magnetic resonance appears at [Formula: see text]. This feature might be useful to detect the gravitational wave with high frequencies.

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Generalized geodesic deviations: a Lagrangean approach

Cited by 3 publications

References 18 publications

Superconductor Meissner Effects for Gravito-Electromagnetic Fields in Harmonic Coordinates Due to Non-Relativistic Gravitational Sources

Superconductor Meissner Effects for Gravito-Electromagnetic Fields in Harmonic Coordinates Due to Non-Relativistic Gravitational Sources

On integrability of the geodesic deviation equation

Higher-order geodesic deviation for charged particles and resonance induced by gravitational waves

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