Related papers: Teukolsky equations, twistor functions, and confor…
The twistor space of the moduli space of solutions of Hitchin's self-duality equations can be identified with the Deligne-Hitchin moduli space of $\lambda$-connections. We use real projective structures on Riemann surfaces to prove the…
Exploiting the special features of four-dimensional Riemannian geometry, we derive topological and rigidity results for hypersurfaces immersed in space forms of dimension 5. First, we provide a complete description of the Weyl tensor for…
We study the Jones and Tod correspondence between selfdual conformal 4-manifolds with a conformal vector field and abelian monopoles on Einstein-Weyl 3-manifolds, and prove that invariant complex structures correspond to shear-free geodesic…
We solve the 2+1-dimensional Teukolsky equation numerically for the Weyl scalars $\psi_0$ and $\psi_4$ along a time-like geodesic approaching the Cauchy horizon of a rapidly rotating perturbed Kerr black hole. We find that both the…
In this paper, the Dirac, twistor and Killing equations on Weyl manifolds with CSpin structures are investigated. A conformal Schr"odinger-Lichnerowicz formula is presented and used to show integrability conditions for these equations. By…
We prove rigidity results for compact Riemannian manifolds in the spirit of Tachibana. For example, we observe that manifolds with divergence free Weyl tensors and $\lfloor \frac{n-1}{2} \rfloor$-nonnegative curvature operators are locally…
Conformal geometry is studied using the unfolded formulation \`a la Vasiliev. Analyzing the first-order consistency of the unfolded equations, we identify the content of zero-forms as the spin-two off-shell Fradkin-Tseytlin module of…
This paper extends the research on the self-consistent effective-one-body theory of a real spinless two-body system based on the post-Minkowskian approximation (Science China, 65, 100411, (2022)) to the case of a binary system for the…
We consider the possibility of deriving a decoupled equation in terms of Weyl tensor components for gravitational perturbations of the Schwarzschild-Tangherlini solution. We find a particular gauge invariant component of the Weyl tensor…
In the class of vacuum Petrov type D spacetimes with cosmological constant, which includes the Kerr-(A)dS black hole as a particular case, we find a set of four-dimensional operators that, when composed {\em off shell} with the Dirac,…
In this article we give general neccessary and sufficient conditions to ensure that a pseudo-Riemannian manifold is conformal to an Einstein space. These conditions are algorithmic in \emph{the metric tensor} whenever the Weyl endomorphism…
A simple procedure is given to construct curved, non-self-dual (complexified) Kaehler metrics on space-time in terms of deformations of holomorphic quadric surfaces in flat twistor space. Imposing Lorentzian reality conditions, the…
We apply the theory of Weyl structures for parabolic geometries developed by A. Cap and J. Slovak in to compute, for a quaternionic contact (qc) structure, the Weyl connection associated to a choice of scale, i.e. to a choice of…
We introduce a correspondence between dimer models (and hence superconformal quivers) and the quantum Teichmuller space of the Riemann surfaces associated to them by mirror symmetry. Via the untwisting map, every brane tiling gives rise to…
We solve the problem of expressing the Weyl scalars $\psi $ that describe gravitational perturbations of a Kerr black hole in terms of Cauchy data. To do so we use geometrical identities (like the Gauss-Codazzi relations) as well as…
We show how the manifold $T^*SU(2, 2)$ arises as a symplectic reduction from eight copies of the twistor space. Some of the constraints in the twistor space correspond to an octahedral configuration of twelve complex light rays in the…
The Teukolsky wave equations governing fields of spin 0, $\tfrac{1}{2}$, 1, $\tfrac{3}{2}$, and 2 are generalized to the case of conformally separable solutions for accreting, rotating black holes.
We obtain exact black hole solutions for static and spherically symmetric sources in a Weyl conformal gauge theory of gravity. We consider a quadratic gravitational action built from the Weyl tensor within a dilation geometry. In a…
For $n \geq 1$, the twistor space $\mathfrak{Z}(\mathbb{S}^{2n})$ of the conformal $2n$-sphere is biholomorphic to the Zariski closure, taken in the complex Grassmannian manifold $\mathbf{G}(n+1, 2n+2)$, of the set of graphs of…
Conformally recurrent pseudo-Riemannian manifolds of dimension n>4 are investigated. The Weyl tensor is represented as a Kulkarni-Nomizu product. If the square of the Weyl tensor is nonzero, a covariantly constant symmetric tensor is…