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For the Newtonian \(N\)-body problem at nonnegative energy, we study solution sets selected by the Jacobi--Maupertuis variational principle and by the associated stationary Hamilton--Jacobi equation. We prove a compactness/stability theorem…
Results on the behaviour in the past time direction of cosmological models with collisionless matter and a cosmological constant $\Lambda$ are presented. It is shown that under the assumption of non-positive $\Lambda$ and spherical or plane…
In this work, we obtained exact solutions of Einstein's field equations for plane symmetric cosmological models by assuming that thy admit conformal motion. The space-time geometry of these solutions is found to be nonsingular, non-vacuum…
A nonstatic and circularly symmetric exact solution of the Einstein equations (with a cosmological constant $\Lambda$ and null fluid) in $2+1$ dimensions is given. This is a nonstatic generalization of the uncharged spinless BTZ metric. For…
We study a static spherically symmetric problem with a black hole and radially directed geodesic flows of dark matter. The obtained solutions have the following properties. At large distances, the gravitational field produces constant…
Original abstract: Consider the worldline of a charged particle in a static spacetime. Contraction of the time-translation Killing field with the retarded electromagnetic energy-momentum tensor gives a conserved electromagnetic energy…
The Schwarzschild-deSitter metric is the known solution of Einstein field equations with cosmological constant term for vacuum spherically symmetric space around a point mass M. Recently it has been reported that in a $Lamda$-dominant world…
We initiate a comprehensive study of a set of solutions of topologically massive gravity known as null warped anti-de Sitter spacetimes. These are pp-wave extensions of three-dimensional anti-de Sitter space. We first perform a careful…
Metric $f(R)$ gravity theories are conformally equivalent to models of quintessence in which matter is coupled to dark energy. We derive a condition for stable tracker solution for metric $f(R)$ gravity in the Einstein frame. We find that…
One of the longstanding problems of modern gravitational physics is the detection of gravitational waves, for which the standard theoretical analysis relies upon the split of the space-time metric into a background metric plus perturbation.…
The Robinson-Trautman solution in the Einstein-Maxwell-$\Lambda$ system admits a shear-free and twist-free null geodesic congruence with a nonvanishing expansion. Restricting to the case where the Maxwell field is aligned, i.e., the…
We show that a spacetime satisfying the linearized vacuum Einstein equations around a type D background is generically of type I, and that the splittings of the Principal Null Directions (PNDs) and of the degenerate eigenvalue of the Weyl…
Negative mass makes perfect physical sense as long as the dominant energy condition is satisfied by the corresponding energy-momentum tensor. Heretofore, only {\it configurations} of negative mass had been found…
In this paper, we consider vacuum asymptotically anti-de Sitter spacetimes $( \mathscr{M}, g )$ with conformal boundary $( \mathscr{I}, \mathfrak{g} )$. We establish a correspondence, near $\mathscr{I}$, between such spacetimes and their…
In the context of $f(R)$ theories of gravity, we address the problem of finding static and spherically symmetric black hole solutions. Several aspects of constant curvature solutions with and without electric charge are discussed. We also…
We consider gravity in 2+1 dimensions in presence of extended stationary sources with rotational symmetry. We prove by direct use of Einstein's equations that if i) the energy momentum tensor satisfies the weak energy condition, ii) the…
Einstein originally proposed a nonsymmetric tensor field, with its symmetric part associated with the spacetime metric and its antisymmetric part associated with the electromagnetic field, as an approach to a unified field theory. Here we…
General equations of the unified field theory, obtained using the curved and torsional space-time, are presented. They contain only independent geometrical parameters (metric and connections) of the metric-affine space, and describe the…
We derive the asymptotic solutions for vacuum spacetimes with non-zero cosmological constant $\Lambda$, using the Newman-Penrose formalism. Our approach is based exclusively on the physical spacetime, i.e. we do not explicitly deal with…
We study the exact solution of Einstein's field equations consisting of a ($n+2$)-dimensional static and hyperplane symmetric thick slice of matter, with constant and positive energy density $\rho$ and thickness $d$, surrounded by two…