Related papers: Proper conformal symmetries in SD Einstein spaces

This paper is the initial part of a comprehensive study of spacetimes that admit the canonical forms of Killing tensor in General Relativity. The general scope of the study is to derive either new exact solutions of Einstein's equations…

An exhaustive list of four-dimensional $\Lambda$-vacuum spacetimes admitting a Killing vector whose self-dual Killing two-form ${\cal F}$ is null is obtained assuming that the self-dual Weyl tensor is proportional to the tensor product of…

Listing has recently extended results of Kozameh, Newman and Tod for four-dimensional spacetimes and presented a set of necessary and sufficient conditions for a metric to be locally conformally equivalent to an Einstein metric in all…

We investigate a class of cylindrically symmetric inhomogeneous $\Lambda$-dust spacetimes which have a regular axis and some zero expansion component. For $\Lambda\ne 0$, we obtain new exact solutions to the Einstein equations and show that…

We consider a model with two real Maxwell fields (or equivalently, a complex Maxwell field) minimally coupled to Einsteins gravity with a negative cosmological constant in four spacetime dimensions. Assuming a specific harmonic dependence…

We determine the submaximal dimensions of the spaces of almost Einstein scales and normal conformal Killing fields for connected conformal manifolds. The results depend on the signature and dimension $n$ of the conformally nonflat conformal…

We develop a new method in order to classify the Bianchi I spacetimes which admit conformal Killing vectors (CKV). The method is based on two propositions which relate the CKVs of 1+(n-1) decomposable Riemannian spaces with the CKVs of the…

In this paper, we use the Killing vector method to formulate the de Sitter/Anti-de Sitter invariant special relativity (dS/AdS-SR). Through solving the Einstein equation with $\Lambda\neq 0$, the basic inertial metric for dS/AdS-SR is…

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 derive some necessary conditions on a Riemannian metric $(M, g)$ in four dimensions for it to be locally conformal to K\"ahler. If the conformal curvature is non anti--self--dual, the self--dual Weyl spinor must be of algebraic type $D$…

We address the problem of how to characterise when a rank-two conformal Killing tensor is the trace-free part of a Killing tensor for a metric in the conformal class. We call such a metric a Killing scale. Our approach is via differential…

We extend the following result of Cochran ``A closed $m$-quasi Einstein manifold ($M,g,X$) with $m \ne -2$ has constant scalar curvature if and only if $X$ is Killing" covering the missing accidental case $m=-2$ and generalize it showing…

For conformally invariant gravity theories defined on Riemannian spacetime and having the Schwarzschild--de-Sitter (SdS) metric as a solution in the Einstein gauge, we consider whether one may conformally rescale this solution to obtain…

Conformal Killing forms are a natural generalization of conformal vector fields on Riemannian manifolds. They are defined as sections in the kernel of a conformally invariant first order differential operator. We show the existence of…

Interior solutions of Einstein's equations with a non-zero cosmological constant are given for static and spherically symmetric configurations of uniform density. The metric tensor and pressure are determined for both positive and negative…

We give a complete proof of the result stated in an earlier article, that the general Einstein metric with a symmetry, an anti-self-dual Weyl tensor and nonzero scalar curvature is determined by a solution of the $SU(\infty)$-Toda field…

We show that every conformal vector field on a Damek-Ricci space is necessarily Killing, establishing a strong form of infinitesimal conformal rigidity. Although this rigidity phenomenon is classically known in the Einstein setting, our…

We present a new two-parameter family of solutions of Einstein gravity with negative cosmological constant in 2+1 dimensions. These solutions are obtained by squashing the anti-de Sitter geometry along one direction and posses four Killing…

We study first and second order conformal symmetries of the Yamabe Laplacian on a general pseudo-Riemannian manifold and of the Paneitz operator on Einstein spaces. We show that first order conformal symmetries of the Yamabe operator induce…

We show how to lift solutions of Euclidean Einstein-Maxwell equations with non-zero cosmological constant to solutions of eleven-dimensional supergravity theory with non-zero fluxes. This yields a class of 11D metrics given in terms of…