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Kerr Scattering Coefficients via Isomonodromy

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arxiv 1506.06588 v2 pith:WW2PWLJT submitted 2015-06-22 hep-th gr-qc

Bruno Carneiro da Cunha , Fábio Novaes This is my paper · ORCID
classification hep-thgr-qc
keywords scatteringfunctionequationgenericisomonodromykerrpainlevproblem
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abstract

We study the scattering of a massless scalar field in a generic Kerr background. Using a particular gauge choice based on the current conservation of the radial equation, we give a generic formula for the scattering coefficient in terms of the composite monodromy parameter $\sigma$ between the inner and the outer horizons. Using the isomonodromy flow, we calculate $\sigma$ exactly in terms of the Painlev\'e V $\tau$-function. We also show that the eigenvalue problem for the angular equation (spheroidal harmonics) can be calculated using the same techniques. We use recent developments relating the Painlev\'e V $\tau$-function to Liouville irregular conformal blocks to claim that this scattering problem is solved in the combinatorial sense, with known expressions for the $\tau$-function near the critical points.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Projecting Gravitational Fluctuations onto Near-Horizon Throats

    hep-th 2026-08 conditional novelty 7.0 of 10

    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.

  2. Ergodic Hysteresis of the Kerr black hole spectrum

    gr-qc 2025-11 conditional novelty 6.0 of 10

    Near-extremal Kerr black holes with massive scalar fields exhibit a cascade of exceptional points that can adiabatically permute arbitrary quasinormal-mode overtones.

  3. Connecting scattering, monodromy, and MST's renormalized angular momentum for the Teukolsky equation in Kerr spacetime

    gr-qc 2024-12 conditional novelty 6.0 of 10

    The MST renormalized angular momentum for the Kerr Teukolsky equation is exactly related to the monodromy eigenvalues of the irregular singular point at infinity.

  4. Exceptional lines in the Kerr-Newman black hole spectrum

    gr-qc 2026-07 accept novelty 5.5 of 10

    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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