Relativity and Cosmology

    

Some Mathematical Results of Light Path Models in General Relativity and the Decomposition of the Null Geodesic Into Gravitational Components

Authors: Gerald Malczewski

This paper is a natural continuation of an earlier paper of light path models and investigates the mathematical implications of geodesic light trajectories within a Schwarzschild metric gravitational field. We focus on a model expressed as infinite Taylor series expansion and its finite cut-off counterpart. A comparison is then made against another existing model that is expressed in closed form not requiring an infinite series and which requires a Jacobian elliptic function. Under some restriction of the mass of the central gravitating body these different models were previously shown to be equivalent. Using these results, some mathematical relationships are then derived. Additionally, we decompose the light path equation into an infinite set of ‘gravitational components, somewhat akin to techniques used in Fourier analysis.

Comments: 21 Pages. Mathematical corrections have been made but with no material effect on the conclusions.

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Submission history

[v1] 2025-04-02 23:22:04
[v2] 2025-08-28 15:03:53

Unique-IP document downloads: 195 times

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