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28 March 2024
 
  » arxiv » gr-qc/0510066

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Quasinormal modes of plane-symmetric anti-de Sitter black holes: a complete analysis of the gravitational perturbations
Alex S. Miranda ; Vilson T. Zanchin ;
Date 14 Oct 2005
AbstractWe study in detail the quasinormal modes (QNMs) of linear gravitational perturbations of plane-symmetric anti-de Sitter black holes. The wave equations are obtained by means of the Newman-Penrose formalism and the Chandrasekhar transformation theory. We show that oscillatory modes decay exponentially with time such that these black holes are stable against gravitational perturbations. Our numerical results show that in the large (small) black hole regime the frequencies of the ordinary QNMs are proportional to the horizon radius $r_{+}$ (wavenumber $k$). The frequency of the purely damped mode is very close to the algebraically special frequency in the small horizon limit, and goes as $ik^{2}/3r_{+}$ in the opposite limit. This last result is confirmed by an analytical method based on the power series expansion of the frequency in terms of the horizon radius. The same procedure applied to the Schwarzschild anti-de Sitter spacetime proves that the purely damped frequency goes as $i(l-1)(l+2)/3r_{+}$, where $l$ is the quantum number characterizing the angular distribution.
Source arXiv, gr-qc/0510066
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