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Kerr-de Sitter Quasinormal Modes via Accessory Parameter Expansion
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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 $\tau$-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 $\epsilon=(r_{C}-r_{+})/L$, 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 $\epsilon^2$ for general $a$, and up to order $\epsilon^{3}$ with the coefficients expanded up to $(a/L)^{3}$. Similarly, the expansion for the angular eigenvalues is given as a series up to $(a\omega)^{3}$ 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.
Forward citations
Cited by 7 Pith papers
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Projecting Gravitational Fluctuations onto Near-Horizon Throats
A pair of coordinate changes projects Heun-type gravitational fluctuation equations onto two matched hypergeometric problems, reproducing instanton-counting results and yielding Schwarzian zero modes.
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Near-extremal Kerr black holes get a universal (s-1/2) log T_H entropy correction from long-lived modes, derived exactly from Virasoro blocks.
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Decoupling Limit of Quiver Theories and the Angular Spectra of Extreme C-metrics
Angular eigenvalues of the extreme charged C-metric are computed analytically via a confluent limit of SU(2)×SU(2) quiver gauge theory, matching numerical results.
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Ergodic Hysteresis of the Kerr black hole spectrum
Near-extremal Kerr black holes with massive scalar fields exhibit a cascade of exceptional points that can adiabatically permute arbitrary quasinormal-mode overtones.
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One loop corrections to the thermodynamics of near-extremal Kerr-(A)dS black holes from Heun equation
Cold near-extremal Kerr-de Sitter black holes carry universal log(T) entropy corrections while rotating Nariai geometries do not, as derived from Teukolsky/Heun connection coefficients.
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Connecting scattering, monodromy, and MST's renormalized angular momentum for the Teukolsky equation in Kerr spacetime
The MST renormalized angular momentum for the Kerr Teukolsky equation is exactly related to the monodromy eigenvalues of the irregular singular point at infinity.
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Exceptional lines in the Kerr-Newman black hole spectrum
Near-extremal Kerr-Newman black holes host exceptional lines of degenerate (ℓ,m)=(1,1) scalar overtones that induce spectral permutations and link to zero-damping/damped mode branching.
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