Version 1
: Received: 31 August 2023 / Approved: 7 September 2023 / Online: 7 September 2023 (11:21:24 CEST)
How to cite:
Lobo, M.; Carneiro, F. Mapping Geodesic Orbits around Cosmic Strings using Iterated Maps and Correlation with Disclination Intensity. Preprints2023, 2023090529. https://doi.org/10.20944/preprints202309.0529.v1
Lobo, M.; Carneiro, F. Mapping Geodesic Orbits around Cosmic Strings using Iterated Maps and Correlation with Disclination Intensity. Preprints 2023, 2023090529. https://doi.org/10.20944/preprints202309.0529.v1
Lobo, M.; Carneiro, F. Mapping Geodesic Orbits around Cosmic Strings using Iterated Maps and Correlation with Disclination Intensity. Preprints2023, 2023090529. https://doi.org/10.20944/preprints202309.0529.v1
APA Style
Lobo, M., & Carneiro, F. (2023). Mapping Geodesic Orbits around Cosmic Strings using Iterated Maps and Correlation with Disclination Intensity. Preprints. https://doi.org/10.20944/preprints202309.0529.v1
Chicago/Turabian Style
Lobo, M. and Fernando Carneiro. 2023 "Mapping Geodesic Orbits around Cosmic Strings using Iterated Maps and Correlation with Disclination Intensity" Preprints. https://doi.org/10.20944/preprints202309.0529.v1
Abstract
Cosmic strings can arise from spontaneous phase transitions during the inflationary period and are describable as disclination topological defects in spacetime. Analytical integration of the geodesic equations for a particle around a cosmic string reveals distinct orbit patterns dependent on the disclination intensity $\beta_{0}$. After its interaction with the cosmic string, the particle's behavior becomes random. To categorize these patterns, we describe the geodesic motion as iterated maps of a discrete parameter. Through the stabilization values of these functions, we correlate the scattering angle and the number of loops for the particle with $\beta_{0}$. Therefore, we interpret the gravitational field mathematically as an instructor of a particle's next position, given its previous one. We find that the radial function in the small displacement limit is similar to the logistic map. This leads us to conjecture the potential of the discrete parameter being a multiple of Planck's time, suggesting a method for the geometric discretization of spacetime around a cosmic string.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
