Abstract
We give explicit expressions for the finite frequency greybody factor, quasinormal modes, and Love numbers of Kerr black holes by computing the exact connection coefficients of the radial and angular parts of the Teukolsky equation. This is obtained by solving the connection problem of the confluent Heun equation in terms of the explicit expression of irregular Virasoro conformal blocks as sums over partitions via the Alday, Gaiotto, and Tachikawa correspondence. In the relevant approximation limits our results are in agreement with existing literature. The method we use can be extended to solve the linearized Einstein equation in other interesting gravitational backgrounds.
Highlights
AND OUTLOOKThe recent experimental verification of gravitational waves [1] renewed the interest in the theoretical studies of general relativity and black hole physics
The study of exact solutions of differential equations rather than their approximate or numerical solutions is of paramount importance both to deepen our comprehension of physical phenomena and to reveal possible physical fine structure effects
Recent developments in the study of two-dimensional conformal field theories, their relation with supersymmetric gauge theories, equivariant localization and duality in quantum field theory produced new tools which are very effective to study long-standing classical problems in the theory of differential equations. It has been known for a long time that the study of two-dimensional conformal field theories (CFTs) [2] and of the representations of its infinite-dimensional symmetry algebra provide exact solutions to partial differential equations in terms of conformal blocks and the appropriate fusion coefficients
Summary
The recent experimental verification of gravitational waves [1] renewed the interest in the theoretical studies of general relativity and black hole physics. An important example is given by Kerr black hole solutions which asymptote to the (anti–)de Sitter metric at infinity These correspond to the Heun equation, which has four regular singularities on the Riemann sphere, and can be engineered from five-point correlators in Liouville CFT with four primary operator insertions and one level two degenerate field. This will provide explicit formulas for the corresponding connection problem and wave functions allowing for an example to give an exact expression for the greybody factor studied in [48]. It could reveal to be useful for other applications in gravitational problems
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