Related papers: On the Einstein-Weyl and conformal self-duality eq…
We derive master equations for linear perturbations in Einstein-Maxwell-scalar theory, for any spacetime dimension D and any background with a maximally symmetric n = (D - 2)-dimensional spatial component. This is done by expressing all…
Paraconformal or $GL(2)$ geometry on an $n$-dimensional manifold $M$ is defined by a field of rational normal curves of degree $n-1$ in the projectivised cotangent bundle $\mathbb{P} T^*M$. Such geometry is known to arise on solution spaces…
We prove that simply connected Einstein four-manifolds of positive scalar curvature are conformally K\"ahler if and only if the determinant of the self-dual Weyl curvature is positive.
We show that (specifically scaled) equations of shear-free null geodesic congruences on the Minkowski space-time possess intrinsic self-dual, restricted gauge and algebraic structures. The complex eikonal, Weyl 2-spinor, $SL(2,\mathbb C)$…
In this paper, we establish compactness results of some class of conformally compact Einstein 4-manifolds. In the first part of the paper, we improve the earlier results obtained by Chang-Ge. In the second part of the paper, as…
We consider $d$-dimensional solutions to the electrovacuum Einstein-Maxwell equations with the Weyl tensor of type N and a null Maxwell $(p+1)$-form field. We prove that such spacetimes are necessarily aligned, i.e. the Weyl tensor of the…
In three-dimensional Einstein-Maxwell gravity the electrostatic Banados-Teitelboim-Zanelli solution and the magnetostatic Hirschmann-Welch solution are connected by a duality mapping. Here we point out that a similar duality mapping exists…
The hyper-CR Einstein-Weyl structures on $\R^3$ can be described in terms of the solutions to the dispersionless Hirota equation. In the present paper we show that simple geometric constructions on the associated twistor space lead to…
Some properties of the 4-dim Riemannian spaces with metrics $$ ds^2=2(za_3-ta_4)dx^2+4(za_2-ta_3)dxdy+2(za_1-ta_2)dy^2+2dxdz+2dydt $$ associated with the second order nonlinear differential equations $$…
We present a conformal isometry for static extremal black hole solutions in all four-dimensional Einstein-Maxwell-scalar theories with electromagnetic duality groups `of type $E_7$'. This includes, but is not limited to, all supergravity…
We investigate the geometry of a twisting non-shearing congruence of null geodesics on a conformal manifold of even dimension greater than four and Lorentzian signature. We give a necessary and sufficient condition on the Weyl tensor for…
In 2021 Konopelchenko, Schief and Szereszewski observed that solutions of 4D dispersionless Hirota system also solve the general heavenly equation describing self-dual vacuum Einstein metrics in neutral signature. They also noticed that the…
We show that the Teukolsky connection, which defines generalized wave operators governing the behavior of massless fields on Einstein spacetimes of Petrov type D, has its origin in a distinguished conformally and GHP covariant connection on…
On a $3$D manifold, a Weyl geometry consists of pairs $(g, A) =$ (metric, $1$-form) modulo gauge $\widehat{g} = {\rm e}^{2\varphi} g$, $\widehat{A} = A + {\rm d}\varphi$. In 1943, Cartan showed that every solution to the Einstein-Weyl…
We present several new exact solutions in five and higher dimensional Einstein-Maxwell theory by embedding the Nutku instanton. The metric functions for the five-dimensional solutions depend only on a radial coordinate and on two spatial…
Most known four-dimensional cohomogeneity-one Einstein metrics are diagonal in the basis defined by the left-invariant one-forms, though some essentially non-diagonal ones are known. We consider the problem of explicitly seeking…
We prove rigidity and gap theorems for self-dual and even Poincar\'e-Einstein metrics in dimension four. As a corollary, we give an obstruction to the existence of self-dual Poincar\'e-Einstein metrics in terms of conformal invariants of…
Beginning with the self-dual two-forms approach to the Einstein equations, we show how, by choosing basis spinors which are proportional to solutions of the Dirac equation, we may rewrite the vacuum Einstein equations in terms of a set of…
We outline a new geometric method of constructing exact solutions of gravitational field equations parametrized by generic off-diagonal metrics, anholonomic frames and possessing, in general, nontrivial torsion and nonmetricity. 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…