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Revista de Matemática Teoría y Aplicaciones
Print version ISSN 1409-2433
Rev. Mat vol.22 n.2 San José Jul./Dec. 2015
Articles
A visualization of null geodesics for the bonnor massive dipole
Visualización de geodésicas nulas para el dipolo masivo de bonnor
1Escuela de Física, Universidad de Costa Rica. San José, Costa Rica. E-Mail: gandreoliva@gmail.com
2Escuela de Física, Universidad de Costa Rica. San José, Costa Rica. Centro de Investigación en Ciencias Atómicas, Nucleares y Moleculares (CICANUM). E-Mail: jbonatti2011@gmail.com
3Escuela de Física, Universidad de Costa Rica. San José, Costa Rica. E-Mail: ivancg@msn.com
4Centro de Investigaciones Espaciales (CINESPA), Universidad de Costa Rica. San José, Costa Rica. E-Mail: frutos62@gmail.com
In this work we simulate null geodesics for the Bonnor massive dipole metric by implementing a symbolic-numerical algorithm in Sage and Python. This program is also capable of visualizing in 3D, in principle, the geodesics for any given metric. Geodesics are launched from a common point, collectively forming a cone of light beams, simulating a solid-angle section of a point source in front of a massive object with a magnetic field. Parallel light beams also were considered, and their bending due to the curvature of the space-time was simulated.
Keywords: general relativity; geodesics; differential geometry; free software
En este trabajo se simulan geodésicas nulas para la métrica de dipolo masivo de Bonnor, implementando un algoritmo simbólico-numérico en Sage y Python. Este programa es capaz, en principio, de visualizar en 3D las geodésicas de cualquier métrica. Estas geodésicas inician en un punto común, formando colectivamente un cono de rayos de luz, simulando una sección de ángulo sólido de una fuente puntual frente a un objeto masivo con campo magnético. Se consideran también rayos de luz paralelos, y se simuló su cambio de trayectoria debida a la curvatura del espacio-tiempo.
Palabras clave: relatividad general; geodésicas; geometría diferencial; software libre
REFERENCES
Bonatti, J.; Semionova, L.; Páez, J. (1985) "Motion in Melvin metric", Uniciencia 2(1): 13-19. [ Links ]
Bonnor, W.B. (1965) "An exact solution of the Einstein-Maxwell equations referring to a magnetic dipole", Zeitschrift für Physik 190: 444-445. [ Links ]
Ková˘r, J.; Kopácek, O.; Karas, V.; Kojima, Y. (2013) "Regular and chaotic˘ orbits near a massive magnetic dipole", Classical and Quantum Gravity 30(2), 025010. [ Links ]
Müller, T.; Frauendiener, J. (2011) "Studying null and time-like geodesics in the classroom", Eur. J. Phys32 747 doi:10.1088/0143-0807/32/3/011 [ Links ]
Sanabria V., J.D.; Valenzuela, C.A. (2011) "Motion of charged test particles in a static spacetime endowed with magnetic field", Revista Colombiana de Física 43(1), 4 pages. [ Links ]
Scherer, D.; Dubois, P.; Sherwood, B. (2000) "VPython: 3D interactive scientific graphics for students", Computing in Science and Engineering, Sept/Oct. 2000: 82-88. [ Links ]
Received: February 25, 2014; Revised: April 19, 2015; Accepted: May 11, 2015
This is an open-access article distributed under the terms of the Creative Commons Attribution License
