Fetching the paper…

Reading the bibliography…

2015

The Jacobi-metric for timelike geodesics in static spacetimes

Gibbons, G. W.

Original
PDF
Post on X

Understand

It is shown that the free motion of massive particles moving in static spacetimes are given by the geodesics of an energy-dependent Riemannian metric on the spatial sections analogous to Jacobi's metric in classical dynamics.

In the massless limit Jacobi's metric coincides with the energy independent Fermat or optical metric.
For stationary metrics, it is known that the motion of massless particles is given by the geodesics of an energy independent Finslerian metric of Randers type.
The motion of massive particles is governed by neither a Riemannian nor a Finslerian metric.

The Jacobi-metric for timelike geodesics in static spacetimes · Around

Built on

G. W. Gibbons “Editorial note to: Ludwig Flamm, Contributions to Einstein’s theory of gravitation” Gen Relativ Gravit (2015) 47
1907
Earlier work this paper cites.
L. Flamm “ Beiträge zur Einsteinschen Gravitationstheorie” Physikalische Zeitschrift 17
1916
Earlier work this paper cites.
Sir G. Greenhill, “Newton-Einstein planetary orbit,” Phil. Mag
1921
Earlier work this paper cites.
R. F. Baierlein, D. H. Sharp and J. A. Wheeler, Three-Dimensional Geometry as Carrier of Information about Time, Phys. Rev. 126
1962
Earlier work this paper cites.
O. C. Onge Curvature and Mechanics
1975
Earlier work this paper cites.
V. G. Gurzadyan and G. K. Savvidy Collective relaxation of stellar systems
1986
Earlier work this paper cites.

Similar

V. G. Gurzadyan and A.A. Kocharyan, The Arnowitt-Deser-Misner principle and geodesic flows in Wheeler-De-Witt superspace, Zeksp. Teor. Fiz
1987
Cited alongside, same era.
G. W. Gibbons, No glory in cosmic string theory
1993
Cited alongside, same era.
N. J. Cornish and G. W. Gibbons, The Tale of two centers
1997
Cited alongside, same era.
G. W. Gibbons and M. C. Werner, Applications of the Gauss-Bonnet theorem to gravitational lensing
Original
2008
Cited alongside, same era.
G. W. Gibbons and C. M. Warnick, Universal properties of the near-horizon optical geometry
Original
2009
Cited alongside, same era.
G. W. Gibbons, C. A. R. Herdeiro, C. M. Warnick and M. C. Werner, Stationary Metrics and Optical Zermelo-Randers-Finsler Geometry

Then

M. Banados, J. Silk and S. M. West, “Kerr Black Holes as Particle Accelerators to Arbitrarily High Energy,” Phys. Rev. Lett. 103
Original
2009
Later among the works it cites.
M. Pettini, Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics
2010
Later among the works it cites.
M. C. Werner, Gravitational lensing in the Kerr-Randers optical geometry
2012
Later among the works it cites.
G. W. Gibbons and M. Vyska, “The Application of Weierstrass elliptic functions to Schwarzschild Null Geodesics,” Class. Quant. Grav. 29
Original
2012
Later among the works it cites.
M. Cvetic and G. W. Gibbons, Annals Phys. 327
Original
2012
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

2009

Cited alongside, same era.

M. Biesiada and S. E. Rugh, Maupertuis principle, Wheeler’s superspace and an invariant criterion for local instability in general relativity, gr-qc/9408030

Cited in the paper.

C. Bloomer, Optical Geometry of the Kerr Space-time

Cited in the paper.

G. Muñoz, “Orbits of massless particles in the Schwrazschild metric: Exact solutions,” A. J. Phys 82

2014

Later among the works it cites.