Relativity and Cosmology

    

Power Series Solution for Photon Trajectories In Static Stationary Spherically Symmetric Gravitational Field

Authors: Mark Timothy Sheldrick

Here a simple power series solution for the path of a photon in a static, stationary spherically symmetric gravitational field in a vacuum (described by the Schwarzschild solution) is derived in the form of a power series of the angular coordinate () of the photon around the axis in spherical coordinates (r,,). Standard results for photon trajectories under the influence of gravity are derived by this method. The series solution simplifies where there is a part of the trajectory with a zero first derivative (tangent) and simplifies in a different way when the trajectory crosses the r=3m radius.

Comments: 14 Pages.

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Submission history

[v1] 2014-07-31 11:24:23

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