Jacobi-Maupertuis Randers-Finsler metric for curved spaces and the gravitational magnetoelectric effect

Chanda, Sumanto; Gibbons, G. W.; Guha, Partha; Maraner, Paolo; Werner, Marcus C.

doi:10.48550/arxiv.1903.11805

Cited by 7 publications

(14 citation statements)

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“…However, the method has some difficulties when applied to stationary spacetimes . The most prominent of them was that the geodesic structure of spacetime was not inherited completely [4].…”

Section: Discussion and Final Remarksmentioning

confidence: 99%

“…For the case of spherically symmetric space this is related with the fact that the Clairaut constant (the momentum) is conserved and therefore, without lose of generality it suffices to consider the ecuatorial plane θ = π 2 . However, when we consider an stationary spacetime we can not do the same reduction, and that is the reason why the previous attempts have given only partial answers to the problem of finding a Jacobi metric that inherits the geodesics [2,4]. Indeed, the Jacobi metrics proposed in the previous works inherit other properties, but it is not possible to recover from them the geodesic equations, for example.…”

Section: The New Jacobi Metricmentioning

confidence: 96%

“…The extension to time dependent and stationary metrics were studied in [3,4]. The formalism was also applied to charged black holes [5] and wormholes [6].…”

Section: Introductionmentioning

confidence: 99%

“…The formalism worked well when dealing with static, spherically symmetric, asymptotically flat spacetimes and with time dependent asymptotically flat metrics. However, when dealing with stationary spacetimes the method does not give a Jacobi metric that inherits the dynamics [4].…”

Section: Introductionmentioning

confidence: 99%

“…However, the Jacobi metric provided for stationary spacetimes does not inherit the goedesics of the spacetime metric. In [4] the authors provide a different Jacobi metric for stationary spacetimes, but this metric neither does inherit all the geodesic properties.…”

Section: Introductionmentioning

confidence: 99%

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The generalized Jacobi metric

Argañaraz¹,

Andino²

2021

Preprint

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We present a new approach to the Jacobi metric formalism for Lorentzian spacetimes. We define a new Jacobi metric that inherits the spacetime, null and timelike geodesic equations for asymptotically flat spacetimes including the stationary ones. The method provides a way for finding a reduced 2-dimensional Jacobi metric, which in the static spherically symmetric case coincides with the already known Jacobi metric. We discuss about the conserved quantities for both proposals. Applying this formalism to black hole metrics, we show that the Gaussian curvature of the reduced 2-dimensional Jacobi metric attains an extremum at the points where the horizons are located giving one of the first characterizations of horizons in a Riemannian metric coming from a spacetime.

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“…However, the method has some difficulties when applied to stationary spacetimes . The most prominent of them was that the geodesic structure of spacetime was not inherited completely [4].…”

Section: Discussion and Final Remarksmentioning

confidence: 99%

Section: The New Jacobi Metricmentioning

confidence: 96%

“…The extension to time dependent and stationary metrics were studied in [3,4]. The formalism was also applied to charged black holes [5] and wormholes [6].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The generalized Jacobi metric

Argañaraz¹,

Andino²

2021

Preprint

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Dynamics in wormhole spacetimes: a Jacobi metric approach

Argañaraz

Andino

2020

Class. Quantum Grav.

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This article deals with the study of the dynamics of particles in different wormhole geometries. Using the Jacobi metric approach we study the geodesic motion on the Morris–Thorne wormhole. We found the only stable circular orbit located at the throat. We show that the Gaussian curvature of the Jacobi metric is directly related with the wormhole flare-out condition. We provide a simple test for determining the existence of a throat in a spacetime by using the Gaussian curvature of the associated Jacobi metric only. We discuss about the trajectories in the Kepler problem in a wormhole background. Finally, we discuss about the restrictions over the stress–energy tensor imposed by the existence of elliptic orbits in the Kepler problem.

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Finslerian geometrization of quantum mechanics in the hydrodynamical representation

2019

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We consider a Finslerian type geometrization of the non-relativistic quantum mechanics in its hydrodynamical (Madelung) formulation, by also taking into account the effects of the presence of the electromagnetic fields on the particle motion. In the Madelung representation the Schrödinger equation can be reformulated as the classical continuity and Euler equations of classical fluid mechanics in the presence of a quantum potential, representing the quantum hydrodynamical evolution equations. The equation of particle motion can then be obtained from a Lagrangian similar to its classical counterpart. After the reparametrization of the Lagrangian it turns out that the Finsler metric describing the geometric properties of quantum hydrodynamics is a Kropina metric. We present and discuss in detail the metric and the geodesic equations describing the geometric properties of the quantum motion in the presence of electromagnetic fields. As an application of the obtained formalism we consider the Zermelo navigation problem in a quantum hydrodynamical system, whose solution is given by a Kropina metric. The case of the Finsler geometrization of the quantum hydrodynamical motion of spinless particles in the absence of electromagnetic interactions is also considered in detail, and the Zermelo navigation problem for this case is also discussed.

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Jacobi-Maupertuis Randers-Finsler metric for curved spaces and the gravitational magnetoelectric effect

Cited by 7 publications

References 0 publications

The generalized Jacobi metric

The generalized Jacobi metric

Dynamics in wormhole spacetimes: a Jacobi metric approach

Finslerian geometrization of quantum mechanics in the hydrodynamical representation

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