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Home > Journal of High Energy Physics (Springer/SISSA) > Kerr-de Sitter quasinormal modes via accessory parameter expansion |

Novaes, Fábio (0000 0000 9687 399X, International Institute of Physics, Federal University of Rio Grande do Norte, Campus Universitário, Lagoa Nova, Natal, RN, 59078-970, Brazil) ; Marinho, Cássio (0000 0004 0643 8134, Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, CEP 22290-180, Brazil) ; Lencsés, Máté (0000 0000 9687 399X, International Institute of Physics, Federal University of Rio Grande do Norte, Campus Universitário, Lagoa Nova, Natal, RN, 59078-970, Brazil) ; Casals, Marc (0000 0004 0643 8134, Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, CEP 22290-180, Brazil) (0000 0001 0768 2743, School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland)

07 May 2019

**Abstract: **Quasinormal modes are characteristic oscillatory modes that control the relaxation of a perturbed physical system back to its equilibrium state. In this work, we calculate QNM frequencies and angular eigenvalues of Kerr-de Sitter black holes using a novel method based on conformal field theory. The spin-field perturbation equations of this background spacetime essentially reduce to two Heun’s equations, one for the radial part and one for the angular part. We use the accessory parameter expansion of Heun’s equation, obtained via the isomonodromic τ -function, in order to find analytic expansions for the QNM frequencies and angular eigenvalues. The expansion for the frequencies is given as a double series in the rotation parameter a and the extremality parameter ϵ = ( r C − r + ) /L , where L is the de Sitter radius and r C and r + are the radii of, respectively, the cosmological and event horizons. Specifically, we give the frequency expansion up to order ϵ 2 for general a , and up to order ϵ 3 with the coefficients expanded up to ( a/L ) 3 . Similarly, the expansion for the angular eigenvalues is given as a series up to ( aω ) 3 with coefficients expanded for small a/L . We verify the new expansion for the frequencies via a numerical analysis and that the expansion for the angular eigenvalues agrees with results in the literature.

**Published in: ****JHEP 1905 (2019) 033**
**Published by: **Springer/SISSA

**DOI: **10.1007/JHEP05(2019)033

**arXiv: **1811.11912

**License: **CC-BY-4.0