Introducción a la relatividad numérica

M. Alcubierre

Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70–543, México D.F. 04510, México

Recibido el 18 de julio de 2005
Aceptado el 14 de marzo de 2005

Resumen

Se presenta una introducción a los conceptos básicos de la relatividad numérica. Partiendo de una breve discusión de la relatividad general, se presenta la formulación 3+1, que es la más utilizada en cálculos numéricos. Se introducen los conceptos de foliación, métrica espacial, funciones de norma y curvatura extrínseca y se discute la separación de las ecuaciones de Einstein que dan lugar a las ecuaciones de Arnowitt–Deser–Misner (ADM). Se menciona también la existencia de formulaciones alternativas de las ecuaciones de evolución y se discute el concepto de hiperbolicidad. Finalmente se presentan las ideas principales de las aproximaciones en diferencias finitas, que son el método mas comúnmente utilizado en relatividad numérica.

Descriptores: Relatividad numérica.

Abstract

I present an introduction to the basic concepts of numerical relativity. Starting from a brief discussion of general relativity, I present the 3+1 formulation, which is the most widely used for numerical calculations in relativity. I introduce the concepts of foliation, spatial metric, gauge functions and extrinsic curvature, and discuss the splitting of Einstein's equations that result in the Arnowitt–Deser–Misner (ADM) equations. I also mention the existence of alternative formulations of the evolution equations and discuss the concept of hyperbolicity. Finally, I discuss the main ideas of finite difference approximations, which are the most common method used in numerical relativity.

Keywords: Numerical relativity.

PACS: 04.20.Ex; 04.25.Dm; 95.30.Sf

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