Abstract
We analyze the Ansatz of separability for Maxwell equations in generically spinning, five-dimensional Kerr-AdS black holes. We find that the parameter μ introduced in [1] can be interpreted as apparent singularities of the resulting radial and angular equations. Using isomonodromy deformations, we describe a non-linear symmetry of the system, under which μ is tied to the Painlevé VI transcendent. By translating the boundary conditions imposed on the solutions of the equations for quasinormal modes in terms of monodromy data, we find a procedure to fix μ and study the behavior of the quasinormal modes in the limit of fast spinning small black holes.
Highlights
We find that the parameter μ introduced in [1] can be interpreted as apparent singularities of the resulting radial and angular equations
We describe a non-linear symmetry of the system, under which μ is tied to the Painleve VI transcendent
By translating the boundary conditions imposed on the solutions of the equations for quasinormal modes in terms of monodromy data, we find a procedure to fix μ and study the behavior of the quasinormal modes in the limit of fast spinning small black holes
Summary
A1 and a2 are two independent rotation parameters This particular form of the metric allows to define an orthonormal 1-form basis eA,. Following [1], to separate the radial and angular equation for the gauge field, we need to construct a special frame with a pair of real null vectors, a pair of complex null vectors and a space-like unit vector orthogonal to all others. They are given as , n, m, m , k as follows r2 + x2 = ∆ (e0 + e1). ( +, −) do not depend on the polar angle θ, and (m+, m−) do not depend on the radial coordinate r
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