Related papers: Generalized Ernst Potentials for arbitrary Dilaton…
We present an exact solution describing a stationary and axisymmetric object with electromagnetic and dilaton fields. The solution generalizes the usual Kerr-Taub-NUT (Newman-Unti-Tamburino) spacetime in general relativity and is obtained…
The integrability structures of the matrix generalizations of the Ernst equation for Hermitian or complex symmetric $d\times d$-matrix Ernst potentials are elucidated. These equations arise in the string theory as the equations of motion…
We argue that all Einstein-Maxwell or Einstein-Proca solutions to general relativity may be used to construct a large class of solutions (involving torsion and non-metricity) to theories of non-Riemannian gravitation that have been recently…
In this thesis we consider several aspects of general relativity relating to exact solutions of the Einstein equations. In the first part gravitational plane waves in the Rosen form are investigated, and we develop a formalism for writing…
For space-times with two spacelike isometries, we present infinite hierarchies of exact solutions of the Einstein and Einstein--Maxwell equations as represented by their Ernst potentials. This hierarchy contains three arbitrary rational…
Recent criticism of higher-dimensional extensions of Einstein's theory is considered. This may have some justification as regards string theory, but is misguided as applied to five-dimensional theories with a large extra dimension. Such…
In the search for exact solutions to Einstein's field equations the main simplification tool is the introduction of spacetime symmetries. Motivated by this fact we develop a method to write the field equations for general matter in a form…
The aim of this paper is to present some structural equations for generalized quasi-Einstein metrics which was defined recently by Catino in [12]. In addition, supposing that the Riemannian manifold is Einstein we shall show that it is a…
Generalized symmetries of the Einstein equations are infinitesimal transformations of the spacetime metric that formally map solutions of the Einstein equations to other solutions. The infinitesimal generators of these symmetries are…
We construct new examples of Einstein metrics by perturbing the conformal infinity of geometrically finite hyperbolic metrics and by applying the inverse function theorem in suitable weighted H\"older spaces.
We investigate a general metric of the Kundt class of spacetimes in higher dimensions. Geometrically, it admits a non-twisting, non-shearing and non-expanding geodesic null congruence. We calculate all components of the curvature and Ricci…
A framework based on an extension of Kaluza's original idea of using a five dimensional space to unify gravity with electromagnetism is used to analyze Maxwell\'{}s field equations. The extension consists in the use of a six dimensional…
Any connection between dark matter and extra dimensions can be cognizably evinced from the associated effective energy-momentum tensor. In order to investigate and test such relationship, a higher dimensional spacetime endowed with a…
A theory of degenerate metrics is developed and applied to the problem of unifying gravitation with electromagnetism. The approach is similar to the Kaluza-Klein approach with a fifth dimension, however no ad hoc conditions are needed to…
We present new exact solutions for the Einstein-Maxwell system in static spherically symmetric interior spacetimes. For a particular form of the gravitational potentials and the electric field intensity, it is possible to integrate the…
After a concise overview of Einstein spacetimes of type II (or more special) in four and five dimensions, we summarize recent results in the six-dimensional case. We assume the optical matrix to be non-degenerate and ``generic'', and the…
We investigate five dimensional Einstein spaces in warped geometries from the point of view of the four dimensional physically relevant Robertson-Walker-Friedman cosmological metric and the Schwarzschild metric. We show that a…
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…
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…
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…