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Title of Journal: Gen Relativ Gravit

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Abbravation: General Relativity and Gravitation

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Springer US

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1572-9532

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Analytical timelike geodesics in Schwarzschild sp

Authors: Uroš Kostić
Publish Date: 2012/01/28
Volume: 44, Issue: 4, Pages: 1057-1072
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Abstract

Timelike orbits in Schwarzschild spacetime are presented and classified in a very transparent and straightforward way into four types The analytical solutions to orbit time and proper time equations are given for all orbit types in the form r = rλ t = tχ and τ= τ χ where λ is the true anomaly and χ is a parameter along the orbit A very simple relation between λ and χ is also shown These solutions are very useful for modelling temporal evolution of transient phenomena near black holes since they are expressed with Jacobi elliptic functions and elliptic integrals which can be calculated very efficiently and accurately

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