Related papers: Three dimensional near-horizon metrics that are Ei…
In a previous paper, we presented new results on non-Riemannian geometry. For an asymmetric connection, we showed that a projective change in the symmetric part generates a vector field that is not arbitrary, but is the gradient of a…
EVH black holes are Extremal black holes with Vanishing Horizon area, where vanishing of horizon area is a result of having a vanishing one-cycle on the horizon. We prove three theorems regarding near horizon geometry of EVH black hole…
The near horizon geometry of extremal rotating black hole in arbitrary dimension possesses SO(2,1)xU(n) symmetry in the special case that all n rotation parameters are equal. We consider a conformal particle associated with such a maximally…
The near horizon geometries are usually constructed by implementing a specific limit to a given extreme black hole configuration. Their salient feature is that the isometry group includes the conformal subgroup SO(2,1). In this work, we…
Einstein-Weyl structures on a three-dimensional manifold $M$ is given by a system $E$ of PDEs on sections of a bundle over $M$. This system is invariant under the Lie pseudogroup $G$ of local diffeomorphisms on $M$. Two Einstein-Weyl…
The geometries with SL$(2,\mathbb{R})$ and some axial U$(1)$ isometries are called ``near-horizon extremal geometries" and are found usually, but not necessarily, in the near-horizon limit of the extremal black holes. We present a new…
We analyse in a systematic way the (non-)compact n-dimensional Einstein Weyl spaces equipped with a cohomogeneity-one metric. With no compactness hypothesis, we prove that, as soon as the (n-1)-dimensional space is an homogeneous reductive…
We consider weighted parallel spinors in Lorentzian Weyl geometry in arbitrary dimensions, choosing the weight such that the integrability condition for the existence of such a spinor, implies the geometry to be Einstein-Weyl. We then use…
We derive a dispersionless integrable system describing a local form of a general three-dimensional Einstein-Weyl geometry with an Euclidean (positive) signature, construct its matrix extension and demonstrate that it leads to the Bogomolny…
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…
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…
In this article, we study Einstein-Weyl structures on almost cosymplectic manifolds. First we prove that an almost cosymplectic $(\kappa,\mu)$-manifold is Einstein or cosymplectic if it admits a closed Einstein-Weyl structure or two…
We construct infinitely many Einstein-Weyl structures on $S^2 \times R$ of signature (-++) which is sufficiently close to the model case of constant curvature, and whose space-like geodesics are all closed. Such structures are obtained from…
We consider local geometry of sub-pseudo-Riemannian structures on contact manifolds. We construct fundamental invariants of the structures and show that the structures give rise to Einstein-Weyl geometries in dimension 3, provided that…
We consider the classification of near-horizon geometries in a general two-derivative theory of gravity coupled to abelian gauge fields and uncharged scalars in four and five dimensions, with one and two commuting rotational symmetries…
We study exact vacuum solutions to quadratic gravity (QG) of the Weyl types N and III. We show that in an arbitrary dimension all Einstein spacetimes of the Weyl type N with an appropriately chosen effective cosmological constant $\Lambda$…
Non-extremal isolated horizons embeddable in 4-dimensional spacetimes satisfying the vacuum Einstein equations with cosmological constant are studied. The horizons are assumed to be stationary to the second order. The Weyl tensor at the…
In this paper we study 4-dimensional $(m,\rho)$-quasi-Einstein manifolds with harmonic Weyl curvature when $m\notin\{0,\pm1,-2,\pm\infty\}$ and $\rho\notin\{\frac{1}{4},\frac{1}{6}\}$. We prove that a non-trivial $(m,\rho)$-quasi-Einstein…
We present a new vacuum solution of Einstein's equations describing the near horizon region of two neutral, extreme (zero-temperature), co-rotating, non-identical Kerr black holes. The metric is stationary, asymptotically near horizon…
We present a parametric study of the spacetime structures obtainable in Weyl conformal gravity's dyonic Reissner-Nordstr\"{o}m solution. We derive expressions for photon sphere radii and horizons for this metric in terms of the conformal…