Related papers: Kramer--Neugebauer Transformation for Einstein--Ma…
The constructed $Sp(4,R)/GL(2,R)$ matrix operator defines the family of isotropic geodesic containing vacuum point lines in the target space of the stationary D=4 Einstein--Maxwell--dilaton--axion theory. This operator is used to derive a…
We consider a class of axially symmetric solutions to Einstein's equations incorporating a $\theta$-dependent scalar field and extend these solutions by introducing electric and magnetic charges via Harrison transformations. Subsequently,…
Starting from a self-dual formulation of gravity, we obtain a noncommutative theory of pure Einstein theory in four dimensions. In order to do that, we use Seiberg-Witten map. It is shown that the noncommutative torsion constraint is solved…
In this paper, we study the \texttt{Ehlers' transformation} (sometimes called gravitational duality rotation) for \texttt{reciprocal} static metrics. First we introduce the concept of reciprocal metric. We prove a theorem which shows how we…
We construct explicitly all extremal instanton solutions to $\mathcal{N}=4,\, D=4$ supergravity truncated to one vector field (Einstein-Maxwell-dilaton-axion (EMDA) theory). These correspond to null geodesics of the target space of the…
The K\"ahler formulation of 5-dimensional Einstein-Kalb-Ramond (EKR) theory admitting two commuting Killing vectors is presented. Three different Kramer-Neugebauer-like maps are established for the 2-dimensional case. A class of solutions…
The non-autonomous chiral model equation for an $m \times m$ matrix function on a two-dimensional space appears in particular in general relativity, where for $m=2$ a certain reduction of it determines stationary, axially symmetric…
Physically admissible choice of the "essential" coordinates identified with components of the metric tensor and co-moving frame of reference reduced to the formulation of the stationary axisymmetric GR problem. Such nontraditional approach…
We present solution generating methods which allow to construct exact static solutions to the equations of four-dimensional Einstein-Maxwell-Dilaton gravity starting with arbitrary static solutions to the pure vacuum Einstein equations,…
We present and discuss a 4-parameter stationary axisymmetric solution of the Einstein-Maxwell equations able to describe the exterior field of a rotating magnetized deformed mass. The solution arises as a system of two overlapping…
Given a solution to 4D Einstein gravity with an isometry direction, it is known that the equations of motion are identical to those of a 3D $\sigma$-model with target space geometry $SU(1,1)/U(1)$. Thus, any transformation by $SU(1, 1)…
The static, plane symmetric solutions and cylindrically symmetric solutions of Einstein-Maxwell equations with a negative cosmological constant are investigated. These black configurations are asymptotically anti-de Sitter not only in the…
We obtain the most general solution of the Einstein electro - vacuum equation for the stationary axially symmetric spacetime in which the Hamilton-Jacobi and Klein - Gordon equations are separable. The most remarkable feature of the…
We use the harmonic maps ansatz to find exact solutions of the Einstein-Maxwell-Dilaton-Axion (EMDA) equations. The solutions are harmonic maps invariant to the symplectic real group in four dimensions $Sp(4,\Rreal)\sim O(5)$. We find…
We consider Einstein-Maxwell-dilaton theory in four dimensions including the Kaluza-Klein theory and obtain the general asymptotic solutions in Bondi gauge. We find that there are three different types of news functions representing…
We construct and study general static, spherically symmetric, magnetically charged solutions in Einstein-Maxwell-dilaton gravity in four dimensions. That is, taking Einstein gravity coupled to a ${\rm U}(1)$ gauge field and a massless…
This paper investigates the integrability properties of Einstein's theory of gravity in the context of accelerating Newman-Unti-Tamburino (NUT) spacetimes by utilizing Ernst's description of stationary and axially symmetric electrovacuum…
We perform full integration of the stationary axisymmetric Einstein-Maxwell-dilaton-axion (EMDA) theory with and without potential using a recently proposed generalization of Carter's approach to spacetimes beyond type D, allowing the…
We consider gauged sigma-models from a Riemann surface into a Kaehler and hamiltonian G-manifold X. The supersymmetric N=2 theory can always be twisted to produce a gauged A-model. This model localizes to the moduli space of solutions of…
L.Huang [Linear Algebra Appl. 331 (2001) 21-30] gave a canonical form of a quaternion matrix $A$ with respect to consimilarity transformations $\tilde{S}^{-1}AS$ in which $S$ is a nonsingular quaternion matrix and $\tilde{h}:=a-bi+cj-dk$…