期刊
CLASSICAL AND QUANTUM GRAVITY
卷 33, 期 2, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/0264-9381/33/2/025004
关键词
black holes; Jacobi metric; geodesics
类别
资金
- STFC [ST/L000636/1] Funding Source: UKRI
- Science and Technology Facilities Council [ST/L000636/1] Funding Source: researchfish
It is shown that the free motion of massive particles moving in static spacetimes is 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 properies of the Jacobi metric for massive particles moving outside the horizon of a Schwarschild black hole are described. By constrast with the massless case, the Gaussian curvature of the equatorial sections is not always negative.
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