Related papers: Teukolsky equations, twistor functions, and confor…

Riemannian Geometry, Topology and Dynamics permit to introduce partially defined holomorphic functions on the variety of representations of the fundamental group of a manifold. The functions we consider are the complex valued Ray-Singer…

We construct a natural conformally invariant one-form of weight $-2k$ on any $2k$-dimensional pseudo-Riemannian manifold which is closely related to the Pfaffian of the Weyl tensor. On oriented manifolds, we also construct natural…

By generalizing and extending some of the earlier results derived by Manin and Merkulov, a twistor description is given of four-dimensional N-extended (gauged) self-dual supergravity with and without cosmological constant. Starting from the…

We consider four (real or complex) dimensional hyper-K\"ahler metrics with a conformal symmetry K. The three-dimensional space of orbits of K is shown to have an Einstein-Weyl structure which admits a shear-free geodesics congruence for…

The LeBrun-Mason twistor correspondences for $S^1$-invariant self-dual Zollfrei metrics are explicitly established. We give explicit formulas for the general solutions of the wave equation and the monopole equation on the de Sitter…

Using the standard Cayley transform and elementary tools it is reiterated that the conformal compactification of the Minkowski space involves not only the "cone at infinity" but also the 2-sphere that is at the base of this cone. We…

Quasinormal modes of usual, four dimensional, Kerr black holes are described by certain solutions of a confluent Heun differential equation. In this work, we express these solutions in terms of the connection matrices for a Riemann-Hilbert…

We discuss the twistor correspondence between complex vector bundles over a self-dual four-dimensional manifold and holomorphic bundles over its twistor space and describe the moduli space of self-dual Yang-Mills fields in terms of Cech and…

We introduce an appropriate formalism in order to study conformal Killing (symmetric) tensors on Riemannian manifolds. We reprove in a simple way some known results in the field and obtain several new results, like the classification of…

The analytical solutions reported in our previous paper are given as series of hypergeometric or Coulomb wave functions. By using them, we can get the Teukolsky functions analytically in a desired accuracy. For the computation, the deep…

The SL(2,R)/U(1) gauged Wess-Zumino-Witten model is an exact conformal field theory describing a black hole in two-dimensional space-time. The free field approach of Bershadsky and Kutasov is a suitable formulation of this CFT in order to…

We study equivariant resolutions and local cohomologies of toric sheaves for affine toric varieties, where our focus is on the construction of new examples of decomposable maximal Cohen-Macaulay modules of higher rank. A result of Klyachko…

The Taub-NUT and Eguchi-Hanson gravitational instantons, along with the self-dual Plebanski-Demianski metric, form a set of Euclidean metrics which can naturally be called `self-dual black holes', as they arise from self-dual slices of the…

In this paper, we establish the asymptotic behaviour along outgoing and incoming radial geodesics, i.e., the peeling property for the tensorial Fackrell-Ipser and spin $\pm 1$ Teukolsky equations on Schwarzschild spacetime. Our method…

In this paper we provide new rigidity results for four-dimensional Riemannian manifolds and their twistor spaces.In particular, using the moving frame method, we prove that $\mathbb{CP}^3$ is the only twistor space whose Bochner tensor is…

We use the manifestly conformally invariant description of a Lorentzian conformal structure in terms of a parabolic Cartan geometry in order to introduce a superalgebra structure on the space of twistor spinors and normal conformal vector…

We introduce an analogue of the composition of the Cherednik and Drinfeld functor for twisted Yangians. Our definition is based on the Howe duality, and originates from the centralizer construction of twisted Yangians due to Olshanski.…

We show how the rigid conformal supersymmetries associated with a certain class of pseudo-Riemannian spin manifolds define a Lie superalgebra. The even part of this superalgebra contains conformal isometries and constant R-symmetries. The…

This is an elementary and self--contained review of twistor theory as a geometric tool for solving non-linear differential equations. Solutions to soliton equations like KdV, Tzitzeica, integrable chiral model, BPS monopole or Sine-Gordon…

We obtain a closed formula for the Kaehler potential of a broad class of four-dimensional Lorentzian or Euclidean conformal "Kaehler" geometries, including the Plebanski-Demianski class and various gravitational instantons such as…