Related papers: On General Solutions for Field Equations in Einste…
The algebra and calculus of generalized differential forms are reviewed and employed to construct a class of generalized connections and to investigate their properties. The class includes generalized connections which are flat when…
A classical problem in general relativity is the Cauchy problem for the linearised Einstein equation (the initial value problem for gravitational waves) on a globally hyperbolic vacuum spacetime. A well-known result is that it is uniquely…
We study a model of the generalized Brans-Dicke gravity presented in both the Jordan and in the Einstein frames, which are conformally related. We show that the scalar field equations in the Einstein frame are reduced to the geodesics…
We find new classes of exact solutions to the Einstein-Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is…
We analyze local anisotropies induced by anholonomic frames and associated nonlinear connections in general relativity and extensions to affine Poincare and de Sitter gauge gravity and different types of Kaluza-Klein theories. We construct…
Based on the distinction between the covariant and contravariant metric tensor components in the framework of the affine geometry approach and also on the choice of the contravariant components, it was shown that a wide variety of third,…
We show that any solution of the 4D Einstein equations of general relativity in vacuum with a cosmological constant may be embedded in a solution of the 5D Ricci-flat equations with an effective 4D cosmological "constant" that is a specific…
We investigate higher dimensional Robinson-Trautman spacetimes with an electromagnetic field aligned with the hypersurface orthogonal, non-shearing, expanding geodesic null congruence. After integrating the system of Einstein-Maxwell…
A generalization of General Relativity is studied. The standard Einstein-Hilbert action is considered in the Palatini formalism, where the connection and the metric are independent variables, and the connection is not symmetric. As a result…
We find possible cosmological models of the Polynomial Affine Gravity described by connections that are either compatible or not with a metric. When possible, we compare them with those of General Relativity. We show that the set of…
The Ernst formulation of the Einstein equations is generalised to accommodate $f(R)$ theories of gravity. It is shown that, as in general relativity, the axisymmetric $f(R)$ field equations for a vacuum spacetime that is either stationary…
The averaging problem in general relativity is briefly discussed. A new setting of the problem as that of macroscopic description of gravitation is proposed. A covariant space-time averaging procedure is described. The structure of the…
In this thesis we take Einstein theory in dimension four seriously, and explore the special aspects of gravity in this number of dimension. Among the many surprising features in dimension four, one of them is the possibility of `Chiral…
We construct explicitly deformations of Einstein's theory of gravity that are consistent and phenomenologically viable since they respect, in particular, cosmological backgrounds. We show that these deformations have unique symmetries in…
The goal of this work is to elaborate on new geometric methods of constructing exact and parametric quasiperiodic solutions for anamorphic cosmology models in modified gravity theories, MGTs, and general relativity, GR. There exist…
We consider 4-dimensional spacetime manifolds that are piecewise Lorentzian, where the Lorentzian components of the manifold are separated by codimension-one planes (spacelike or timelike) on which the metric is degenerate. Such manifolds…
Recently Horava proposed a non-relativistic renormalisable theory of gravitation, which reduces to Einstein's general relativity at large distances, and that may provide a candidate for a UV completion of Einstein's theory. In this paper,…
Quasi-topological terms in gravity can be viewed as those that give no contribution to the equations of motion for a special subclass of metric ans\"atze. They therefore play no r\^ole in constructing these solutions, but can affect the…
The Ba\~nados-Teitelboim-Zanelli (BTZ) black hole metric solves the three-dimensional Einstein's theory with a negative cosmological constant as well as all the generic higher derivative gravity theories based on the metric; as such it is a…
We give an overview of literature related to J\"urgen Ehlers' pioneering 1981 paper on Frame theory--a theoretical framework for the unification of General Relativity and the equations of classical Newtonian gravitation. This unification…