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Kerr-de Sitter quasinormal modes via accessory parameter expansion

  • Fábio NovaesEmail author
  • Cássio I. S. Marinho
  • Máté Lencsés
  • Marc Casals
Open Access
Regular Article - Theoretical Physics
  • 57 Downloads

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 = (rCr+)/L, where L is the de Sitter radius and rC and r+ are the radii of, respectively, the cosmological and event horizons. Specifically, we give the frequency expansion up to order ϵ2 for general a, and up to order ϵ3 with the coefficients expanded up to (a/L)3. Similarly, the expansion for the angular eigenvalues is given as a series up to ()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.

Keywords

Black Holes Classical Theories of Gravity Conformal Field Theory 

Notes

Open Access

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© The Author(s) 2019

Authors and Affiliations

  • Fábio Novaes
    • 1
    Email author
  • Cássio I. S. Marinho
    • 2
  • Máté Lencsés
    • 1
  • Marc Casals
    • 2
    • 3
  1. 1.International Institute of PhysicsFederal University of Rio Grande do Norte, Campus UniversitárioNatalBrazil
  2. 2.Centro Brasileiro de Pesquisas Físicas (CBPF)Rio de JaneiroBrazil
  3. 3.School of Mathematics and StatisticsUniversity College DublinDublin 4Ireland

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