Looking at the Gregory-Laflamme instability through quasinormal modes

Physical review D: Particles and fields (Impact Factor: 4.86). 10/2008; 78(8). DOI: 10.1103/PhysRevD.78.084012
Source: arXiv


We study evolution of gravitational perturbations of black strings. It is well known that for all wave numbers less than some threshold value, the black string is unstable against the scalar type of gravitational perturbations, which is named the Gregory-Laflamme instability. Using numerical methods, we find the quasinormal modes and time-domain profiles of the black string perturbations in the stable sector and also show the appearance of the Gregory-Laflamme instability in the time domain. The dependence of the black string quasinormal spectrum and late-time tails on such parameters as the wave vector and the number of extra dimensions is discussed. There is numerical evidence that at the threshold point of instability, the static solution of the wave equation is dominant. For wave numbers slightly larger than the threshold value, in the region of stability, we see tiny oscillations with very small damping rate. While, for wave numbers slightly smaller than the threshold value, in the region of the Gregory-Laflamme instability, we observe tiny oscillations with very small growth rate. We also find the level crossing of imaginary part of quasinormal modes between the fundamental mode and the first overtone mode, which accounts for the peculiar time domain profiles.

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Available from: Alexander Zhidenko
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    • "However, in higherdimensional spacetimes no one has succeeded in finding such an equation. Recently, there was a certain progress in this problem [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32]. "
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    • "In general, such a Schwarzschild black string suffers from the so-called Gregory-Laflamme instability, namely, long wavelength gravitational instability of the scalar type of the metric perturbations [25, 26]. The Gregory-Laflamme instability has been extensively studied in the last decade [27] [28] and the threshold values of the wavenumber k at which the instability appears are obtained [29]. For the usual scalar, electromagnetic and Dirac field perturbations , the Schwarzschild black string does not meet such a Gregory-Laflamme instability problem. "
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