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Black holes in AdS space
On account of the AdS/CFT correspondence, these quasinormal modes are expected to correspond to perturbations of the dual CFT. The establishment of such a correspondence is hindered by the difficulties in solving the wave equation. In three dimensions, the wave equation is a hypergeometric equation and can therefore be solved [11]. In higher dimensions, the wave equation turns into a Heun equation which is unsolvable. Numerical results have been obtained in four, five and seven dimensions [12]. Dr. Siopsis and S. Musiri developed an analytic method of solving the wave equation, which is in general a Heun equation [13], in the case of a large black hole living in AdS space. The method is based on a perturbative expansion of the wave equation in the dimensionless parameter , where is the frequency of the mode and is the (large) Hawking temperature of the black hole. Such an expansion is no trivial matter, for the dependence of the wavefunction on changes as one moves from the boundary of AdS space to the horizon. The zerothorder approximation was chosen to be an appropriate hypergeometric equation so that higherorder corrections were indeed of higher order in . In three dimensions, this hypergeometric equation is exact. In five dimensions, it was shown that the lowlying quasinormal modes obtained from the zerothorder approximation were in good agreement with numerical results [12]. The firstorder correction was also calculated. The method in [13] may be applied to higher dimensions but the convergence of the perturbative expansion appears to be slower. It would be interesting to examine the implications of this perturbative approach for the AdS/CFT correspondence.
Dr. Siopsis and S. Musiri also investigated an approximation to the wave equation which was valid in the
high frequency regime [14]. In five dimensions they showed that the Heun equation
reduces to a Hypergeometric equation, as in the low frequency regime [13].
They obtained an analytical expression for the asymptotic form of quasinormal frequencies in agreement
with numerical results [12],

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