Timelike and null equatorial geodesics in the
Bonnor-Sackfield relativistic disk
GUILLERMO A. GONZÁLEZ a,*, FRAMSOL LÓPEZ-SUSPESa,b
a Universidad Industrial de Santander, Escuela de Física, Bucaramanga, Colombia.
b Universidad Santo Tomás, Facultad de Telecomunicaciones, Bucaramanga, Colombia.
Abstract. A study of timelike and null equatorial geodesics in the Bonnor- Sackfield relativistic thin disk is presented. The motion of test particles in the equatorial plane is analyzed, both for the newtonian thin disk model as for the corresponding relativistic disk. The nature of the possible orbits is studied by means of a qualitative analysis of the effective potential and by numerically solving the motion equation for radial and non-radial equatorial trajectories. The existence of stable, unstable and marginally stable circular orbits is analyzed, both for the newtonian and relativistic case. Examples of the numerical results, obtained with some simple values of the parameters, are presented.
Keywords: General relativity, exact solutions, equations of motion.
MSC2000: 83Cxx, 83C10, 83C15.
Resumen. En este trabajo se presenta un estudio de las geodésicas temporales y nulas en el disco delgado relativista y newtoniano de Bonnor-Sackfield. Se analiza el movimiento de las partículas de prueba en el plano ecuatorial, tanto para el modelo newtoniano del disco delgado como para el disco relativista correspondiente. La naturaleza de las órbitas posibles se estudia por medio de un análisis cualitativo del potencial efectivo, y numéricamente mediante la solución de la ecuación de movimiento de las trayectorias ecuatorial radial y no radial: Se analiza la existencia de órbitas estables, circulares inestables y estables marginalmente, tanto para el caso newtoniano, como el relativista. Se presentan ejemplos de los resultados numéricos obtenidos con algunos valores de los parámetros simples.
Palabras claves: Relatividad general, soluciones exactas, ecuaciones de movimiento.
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