Related papers: Proper conformal symmetries in SD Einstein spaces
We introduce the notion of metric Lie algebras of Killing type, which are characterized by the fact that all conformal Killing symmetric tensors are sums of Killing tensors and multiples of the metric tensor. We show that if a Lie algebra…
We consider axially symmetric static metrics in arbitrary dimension, both with and without a cosmological constant. The most obvious such solutions have an SO(n) group of Killing vectors representing the axial symmetry, although one can…
We construct new supersymmetric solutions to the Euclidean Einstein-Maxwell theory with a non-vanishing cosmological constant, and for which the Maxwell field strength is neither self-dual or anti-self-dual. We find that there are three…
We discuss Petrov type D Einstein-Maxwell fields in which both double null eigenvectors of the Weyl tensor are non-aligned with the eigenvectors of a non-null electromagnetic field and are assumed to be geodesic, shear-free, diverging and…
In this paper, conformal motions are studied in plane symmetric static spacetimes. The general solution of conformal Killing equations and the general form of the conformal Killing vector for these spacetimes are presented. All…
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 study 4-dimensional Poincar\'e-Einstein manifolds whose conformal class contains a K\"ahler metric. Such Einstein metrics are non-K\"ahler and admit a Killing field extending to the conformal infinity, and the Einstein equation reduces…
We establish an explicit correspondence between two--dimensional projective structures admitting a projective vector field, and a class of solutions to the $SU(\infty)$ Toda equation. We give several examples of new, explicit solutions of…
We discuss smooth metric measure spaces admitting two weighted Einstein representatives of the same weighted conformal class. First, we describe the local geometries of such manifolds in terms of certain Einstein and quasi-Einstein warped…
Gravity coupled three--dimensional $\sigma$--model describing the stationary Einstein--Maxwell--dilaton system with general dilaton coupling is studied. Killing equations for the corresponding five--dimensional target space are integrated.…
Spaces equipped with two complementary (distinct) congruences of self-dual null strings and at least one congruence of anti-self-dual null strings are considered. It is shown that if such spaces are Einsteinian then the vacuum Einstein…
We seek exact solutions to the Einstein field equations which arise when two spacetime geometries are conformally related. Whilst this is a simple method to generate new solutions to the field equations, very few such examples have been…
We identify an anisotropic divergence-free conformal Killing tensor $K_{jl}$ for static spherically symmetric spacetimes, and write the conformal Killing gravity equations as Einstein equations augmented by this tensor. The field equations…
We analyze the space-times admitting two shear-free geodesic null congruences. The integrability conditions are presented in a plain tensorial way as equations on the volume element $U$ of the time-like 2--plane that these directions…
In a recent paper, a new conformally flat metric was introduced, describing an expanding scalar field in a spherically symmetric geometry. The spacetime can be interpreted as a Schwarzschild-like model with an apparent horizon surrounding…
New similarity variables are introduced for the Einstein - Maxwell equations with one Killing vector that reduce the non-linear partial differential equations in three independent variables to ordinary differential equations. These…
Conformal Killing equations and their integrability conditions for nonexpanding hyperheavenly spaces with Lambda are studied. Reduction of ten Killing equations to one master equation is presented. Classification of homothetic and isometric…
We solve the Killing spinor equations of ${\cal N}=1$ supergravity, with four supercharges, coupled to any number of vector and scalar multiplets in all cases. We find that backgrounds with N=1 supersymmetry admit a null, integrable,…
We obtain a coordinate independent algorithm to determine the class of conformal Killing vectors of a locally conformally flat $n$-metric $\gamma$ of signature $(r,s)$ modulo conformal transformations of $\gamma$. This is done in terms of…
We construct infinite-dimensional families of non-singular static space times, solutions of the vacuum Einstein-Maxwell equations with a negative cosmological constant. The families include an infinite-dimensional family of solutions with…