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 σ between the inner and the outer horizons. Using the isomonodromy flow, we calculate σ exactly in terms of the Painleve V τ -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 Painleve V τ -function to Liouville irregular conformal blocks to claim that this scattering problem is solved in the combinatorial sense, with known expressions for the τ -function near the critical points.
Highlights
JHEP11(2015)144 allows us to place boundary conditions such that the two linearly independent solutions of the radial equation correspond to the two solutions involved in the connection problem of the Painleve V equation [27]
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 σ between the inner and the outer horizons
Summary
E., the solution can be written as Φ(xμ) = e−iωteimφR(r)S(θ). T0)θt0 ), where we defined the temperatures T± and angular velocities Ω± for the outer and inner horizons. We define θ∞ = 1 + 2(c0 + ct0) = 1 − 4iM ω = 1 − θ0 − θt0. Eq (2.1) has real coefficients, so if R(r) is a solution, so is R(r)∗. We define the radiation flux as j = −i Q(r)[R(r)∗∂rR(r) − R(r)∂rR(r)∗].
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