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The method based on the Horsky-Mitskievitch conjecture is applied to the Levi-Civita vacuum metric. It is shown, that every Killing vector is connected with a particular class of Einstein-Maxwell fields and each of those classes is found…
The quotient of the conformal group of Euclidean 4-space by its Weyl subgroup results in a geometry possessing many of the properties of relativistic phase space, including both a natural symplectic form and non-degenerate Killing metric.…
The Rainich problem for the Killing-Yano tensors posed by Collinson \cite{col} is solved. In intermediate steps, we first obtain the necessary and sufficient conditions for a 2+2 almost-product structure to determine the principal 2--planes…
We study the free data in the Fefferman-Graham expansion of asymptotically Einstein metrics with non-zero cosmological constant. We prove that if $\mathscr{I}$ is conformally flat, the rescaled Weyl tensor at $\mathscr{I}$ agrees up to a…
We revisit the definition of transverse frames and tetrad choices with regards to its application to numerically generated spacetimes, in particular those from the merger of binary black holes. We introduce the concept of local and…
We present a complete algebraic classification for the curvature tensor in Weyl-Cartan geometry, by applying methods of eigenvalues and principal null directions on its irreducible decomposition under the group of global Lorentz…
The static electrogravitational equations are studied and it is shown that an aligned type D metric which has a Weyl-type relationship between the gravitational and electric potential has shearfree geodesic lines of force. All such fields…
We study null alignment properties of Weyl tensors related via Kaluza$\unicode{x2013}$Klein reduction of vacuum spacetimes by one spatial Killing direction. Kaluza$\unicode{x2013}$Klein reduction is a method that relates spacetimes of…
Extending previous results we show that there are no Petrov type III space-times on which either the Weyl neutrino equation or Maxwell's equations satisfy Huygens' principle. We prove the result by using Maple's NPspinor package to convert…
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…
The use of the bivectors in the General Relativity with Newman-Penrose formalism is important to the description of the exact solutions of the Einstein's field equations. This review is devoted to introduce the basic ideas with calculation…
We present and analyze a class of exact spacetimes which describe accelerating black holes with a NUT parameter. First, we verify that the intricate metric found by Chng, Mann and Stelea in 2006 indeed solves Einstein's vacuum field…
The classification of exact solutions of Maxwell vacuum equations for pseudo-Riemannian spaces with spatial symmetry (homogeneous non-null spaces of Petrov) in the presence of electromagnetic fields invariant with respect to the action of…
In the first part of this thesis, Kerr-Schild metrics and extended Kerr-Schild metrics are analyzed in the context of higher dimensional general relativity. Employing the higher dimensional generalizations of the Newman-Penrose formalism…
Conformal Killing-Yano tensors are introduced as a generalization of Killing vectors. They describe symmetries of higher-dimensional rotating black holes. In particular, a rank-2 closed conformal Killing-Yano tensor generates the tower of…
We construct analytic extensions across the Killing horizons of non-extremal and extremal dipole black rings in Einstein-Maxwell's theory using different methods. We show that these extensions are non-globally hyperbolic, have multiple…
We find necessary and sufficient conditions for a Riemannian four-dimensional manifold $(M, g)$ with anti-self-dual Weyl tensor to be locally conformal to a Ricci--flat manifold. These conditions are expressed as the vanishing of scalar and…
We consider $5$ dimensional electrostatic solutions to Einstein-Maxwell gravity with $2$ commuting spacelike Killing fields. Taking two distinct reductions from $5$ dimensions to a $3$ dimensional base space, we write the Einstein-Maxwell…
We formulate a one-parameter extension of Weyl transformations in first-order gravity and show that it defines a conformally coupled scalar sector with dynamical torsion. The construction reduces to the standard torsionless conformal…
In the standard Einstein's theory the exterior gravitational field of any static and axially symmetric stellar object can be described by means of a single function from which we obtain a metric into a four-dimensional space-time. In this…