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Keywords = modal transseries

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15 pages, 398 KiB  
Article
Exact Solution for Relativistic Trajectories Using Modal Transseries
by Luis Acedo, Abraham J. Arenas and Nicolas De La Espriella
Symmetry 2020, 12(9), 1505; https://doi.org/10.3390/sym12091505 - 13 Sep 2020
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Abstract
In this article, we design a novel method for finding the exact solution of the geodesic equation in Schwarzschild spacetime, which represents the trajectories of the particles. This is a fundamental problem in astrophysics and astrodynamics if we want to incorporate relativistic effects [...] Read more.
In this article, we design a novel method for finding the exact solution of the geodesic equation in Schwarzschild spacetime, which represents the trajectories of the particles. This is a fundamental problem in astrophysics and astrodynamics if we want to incorporate relativistic effects in high precision calculations. Here, we show that exact analytical expressions can be given, in terms of modal transseries for the spiral orbits as they approach the limit cycles given by the two circular orbits that appear for each angular momentum value. The solution is expressed in terms of transseries generated by transmonomials of the form enθ, n=1, 2, , where θ is the angle measured in the orbital plane. Examples are presented that verify the effect of the solutions. Full article
(This article belongs to the Section Physics)
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