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We study time-dependent compactification of extra dimensions. We assume that the spacetime is spatially homogeneous, and solve the vacuum Einstein equations without cosmological constant in more than three dimensions. We consider globally…
We give a formulation of the vacuum Einstein equations in terms of a set of volume-preserving vector fields on a four-manifold ${\cal M}$. These vectors satisfy a set of equations which are a generalisation of the Yang-Mills equations for a…
In this paper we investigate spherically symmetric vacuum solutions of $f(R)$ gravity in a higher dimensional spacetime. With this objective we construct a system of non-linear differential equations, whose solutions depend on the explicit…
We present the solution space of the field equations in the Einstein-aether theory for the case of a vacuum Bianchi Type V space-time. We also find that there are portions of the initial parameters space for which no solution is admitted by…
The problem of comparison of the stationary axisymmetric vacuum solutions obtained within the framework of exact and approximate approaches for the description of the same general relativistic systems is considered. We suggest two ways of…
It is shown that four dimensional vacuum Einstein solutions simply embedded in five dimensions obey the Gauss-Bonnet-Einstein field equations: $G_{ab}+\alpha GB_{ab}+\delta^{55}_{ab}\alpha\exp(-2\chi/\sqrt{\alpha})GB_4=0$ and the…
A method for the search of exact solutions for equation of a nonlocal scalar field in a non-flat metric is considered. In the Friedmann-Robertson-Walker metric the proposed method can be used in the case of an arbitrary potential, with the…
We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of nonlinear partial differential equations. By introducing a new…
We consider a radiating shear-free spherically symmetric metric in higher dimensions. Several new solutions to the Einstein's equations are found systematically using the method of Lie analysis of differential equations. Using the five Lie…
In the macroscopic gravity approach to the averaging problem in cosmology, the Einstein field equations on cosmological scales are modified by appropriate gravitational correlation terms. We present exact cosmological solutions to the…
Extended gravitational models have gained large attention in the last couple of decades. In this work, we examine the solution space of vacuum, static, and spherically symmetric spacetimes within $F(R)$ theories, introducing novel methods…
The Schwarzschild solution is a complete solution of Einstein's field equations for a static spherically symmetric field. The Einstein's field equations solutions appear in the literature, but in different ways corresponding to different…
We propose a general method for solving exactly the static field equations of Einstein and Einstein-Maxwell gravity minimally coupled to a scalar field. Our method starts from an ansatz for the scalar field profile, and determines, together…
We present the 3+1 decomposition of the Simon-Mars tensor, which has the property of being identically zero for a vacuum and asymptotically flat spacetime if and only if the latter is locally isometric to the Kerr spacetime. Using this…
We revisit the problem of solving the Einstein constraint equations in vacuum by a new method, which allows us to prescribe four scalar quantities, representing the full dynamical degrees of freedom of the constraint system. We show that…
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…
Very recently Harada proposed a gravitational theory which is of third order in the derivatives of the metric tensor with the property that any solution of Einstein's field equations (EFEs) possibly with a cosmological constant is…
The Lense--Thirring spacetime describes a 4-dimensional slowly rotating approximate solution of vacuum Einstein equations valid to a linear order in rotation parameter. It is fully characterized by a single metric function of the…
The Einstein-Maxwell equations in D-dimensions admitting (D-3) commuting Killing vector fields have been investigated. The existence of the electric, magnetic and twist potentials have been proved. The system is formulated as the harmonic…
We investigate the vacuum and charged spherically symmetric static solutions of the Einstein equations on cosmological background. The background metric is not flat, but curved, with constant - curvature spatial sections. Both vacuum and…