Stability study of a model for the Klein–Gordon equation in Kerr space-time

The current early stage in the investigation of the stability of the Kerr metric is characterized by the study of appropriate model problems. Particularly interesting is the problem of the stability of the solutions of the Klein–Gordon equation, describing the propagation of a scalar field of mass i...

Full description

Saved in:
Bibliographic Details
Published inGeneral relativity and gravitation Vol. 45; no. 1; pp. 203 - 227
Main Authors Beyer, Horst Reinhard, Alcubierre, Miguel, Megevand, Miguel, Degollado, Juan Carlos
Format Journal Article
LanguageEnglish
Published Boston Springer US 2013
Subjects
Astronomy
Astrophysics and Cosmology
Classical and Quantum Gravitation
Differential Geometry
Mathematical and Computational Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Research Article
Theoretical
Kerr metric
Massive field
Instability
Stability
Klein–Gordon equation
Kerr background
Online AccessGet full text

Cover

More Information
Summary:The current early stage in the investigation of the stability of the Kerr metric is characterized by the study of appropriate model problems. Particularly interesting is the problem of the stability of the solutions of the Klein–Gordon equation, describing the propagation of a scalar field of mass in the background of a rotating black hole. Rigorous results prove the stability of the reduced, by separation in the azimuth angle in Boyer–Lindquist coordinates, field for sufficiently large masses. Some, but not all, numerical investigations find instability of the reduced field for rotational parameters extremely close to . Among others, the paper derives a model problem for the equation which supports the instability of the field down to .
ISSN:0001-7701
1572-9532
DOI:10.1007/s10714-012-1470-0