The three dynamical fates of Boson Stars
F.S. Guzmán
Instituto de Física y Matemáticas, Universidad Michoacána de San Nicolás de Hidalgo, Edificio C–3, Cd. Universitaria, 58040 Morelia, Michoacán, México.
Recibido el 26 de mayo de 2009
Aceptado el 30 de junio de 2009
Abstract
In this manuscript the three types of late–time behavior of spherically symmetric Boson Stars are presented, namely: stable configurations, unstable bounded that collapse and form black holes and unstable unbounded that explode. These three possibilities have been predicted by perturbation theory and other analytical results, whereas the full non–linear evolution of Boson Star configurations has verified the stable and unstable bounded cases using numerical relativity. In this paper also the unbounded case is confirmed to happen. In order to do so, Boson Star solutions are used as initial data of the Einstein–Klein–Gordon system of equations formulated as a constrained initial value problem, which in turn is solved using the finite differences approximation.
Keywords: Boson systems; numerical relativity; self–gravitating systems.
Resumen
En este trabajo se presentan los tres tipos de comportamiento temporal de estrellas de bosones esfericamente simétricas, es decir: configuraciones estables, inestables que colapsan para formar agujeros negros e inestables que explotan. Estas tres posibilidades han sido predichas por la teoría de perturbaciones y otros resultados analíticos, mientras que la evolución no–lineal de las configuraciones de estrellas de bosones ha verificado los casos estable e inestable acotado usando relatividad numérica. En este artículo se confirma además el caso inestable no acotado. Para tal efecto, las soluciones de estrellas de bosones se usan como datos iniciales del sistema de ecuaciones de Einstein–Klein–Gordon formulado como un problema de valores iniciales con evolución restringiuda que resolvemos usando la aproximación con diferencias finitas.
Descriptores: Sistemas bosónicos; relatividad numérica; sistemas autogravitantes.
PACS: 05.30.Jp; 04.25.D–; 04.40.–b
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Acknowledgments
This work is partly supported by projects CIC–UMSNH–4.9, CONACyT 79995 and PROMEP–UMICH–CA–22.
A Kretschmann invariant
We use the central value of the Kretschmann invariant, in order to easily see the formation of a singularity. The expression for the metric (8) is:
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