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Artículo

Well-posedness, linear perturbations, and mass conservation for the axisymmetric Einstein equations

Dain, Sergio AlejandroIcon ; Ortiz, Omar Eduardo
Fecha de publicación: 26/02/2010
Editorial: American Physical Society
Revista: Physical Review D: Particles, Fields, Gravitation and Cosmology
ISSN: 1550-7998
e-ISSN: 1550-2368
Idioma: Inglés
Tipo de recurso: Artículo publicado
Clasificación temática:
Física de Partículas y Campos

Resumen

For axially symmetric solutions of Einstein equations there exists a gauge which has the remarkable property that the total mass can be written as a conserved, positive definite, integral on the spacelike slices. The mass integral provides a nonlinear control of the variables along the whole evolution. In this gauge, Einstein equations reduce to a coupled hyperbolic-elliptic system which is formally singular at the axis. As a first step in analyzing this system of equations we study linear perturbations on a flat background. We prove that the linear equations reduce to a very simple system of equations which provide, though the mass formula, useful insight into the structure of the full system. However, the singular behavior of the coefficients at the axis makes the study of this linear system difficult from the analytical point of view. In order to understand the behavior of the solutions, we study the numerical evolution of them. We provide strong numerical evidence that the system is well-posed and that its solutions have the expected behavior. Finally, this linear system allows us to formulate a model problem which is physically interesting in itself, since it is connected with the linear stability of black hole solutions in axial symmetry. This model can contribute significantly to solve the nonlinear problem and at the same time it appears to be tractable.
Palabras clave: MASS , CONSERVATION , AXIALSYMMETRY , WELL-POSEDNESS
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info:eu-repo/semantics/openAccess Excepto donde se diga explícitamente, este item se publica bajo la siguiente descripción: Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Unported (CC BY-NC-SA 2.5)
Identificadores
URI: http://hdl.handle.net/11336/190234
URL: http://link.aps.org/doi/10.1103/PhysRevD.81.044040
DOI: http://dx.doi.org/10.1103/PhysRevD.81.044040
Colecciones
Articulos(IFEG)
Articulos de INST.DE FISICA ENRIQUE GAVIOLA
Citación
Dain, Sergio Alejandro; Ortiz, Omar Eduardo; Well-posedness, linear perturbations, and mass conservation for the axisymmetric Einstein equations; American Physical Society; Physical Review D: Particles, Fields, Gravitation and Cosmology; 81; 4; 26-2-2010; 1-20
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