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We study static cylindrically symmetric vacuum solutions in Weyl coordinates in the context of the metric f(R) theories of gravity. The set of the modified Einstein equations is reduced to a single equation and it is shown how one can…
In this article, a cylindrical symmetry and static solution of the Einstein's field equations, was presented. The space-time is conformally flat, regular everywhere except on the symmetry axis where it possesses a naked curvature…
The spherically symmetric, static spacetime generated by a crossflow of non-interacting radiation streams, treated in the geometrical optics limit (null dust) is equivalent to an anisotropic fluid forming a radiation atmosphere of a star.…
We present a new geometric approach to the study of static isolated general relativistic systems for which we suggest the name geometrostatics. After describing the setup, we introduce localized formulas for the ADM-mass and ADM/CMC-center…
In this article we study self-gravitating static solutions of the Einstein-ScalarField system in arbitrary dimensions. We discuss the existence and the non-existence of geodesically complete solutions depending on the form of the scalar…
We have studied the closed universe model with the variable cosmological term, which is presented as a sum of two terms: Lambda=Lambda_0 -k R. First term Lambda_0 is a constant and it is describing a sum of quantum field's zero…
We illustrate, through a series of prototypical examples, that linear parity-time (PT) symmetric lattices with extended gain/loss profiles are generically unstable, for any non-zero value of the gain/loss coefficient. Our examples include a…
The paper is a study of geodesic in two-dimensional pseudo-Riemannian metrics. Firstly, the local properties of geodesics in a neighborhood of generic parabolic points are investigated. The equation of the geodesic flow has singularities at…
We consider planar directed last-passage percolation on the square lattice with general i.i.d. weights and study the geometry of the full set of semi-infinite geodesics in a typical realization of the random environment. The structure of…
The general stationary cylindrically symmetric solution of Einstein-massless scalar field system with a non-positive cosmological constant is presented. It is shown that the general solution is characterized by four integration constants.…
We consider geodesics motion in a particular Kundt type III spacetime in which Einstein-Yang-Mills equations admit solutions. On a particular surface as constraint we project the geodesics into the (x,y) plane and treat the problem as a…
This paper presents an analytical study of the behavior of radial free-geodesics in the Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetime within the Lambda Cold Dark Matter ({\Lambda}CDM) model. Using the radial free motion solutions,…
In the homogeneous metric of Som-Raychaudhuri, in general relativity, we study the three types of geodesics: timelike, null, and spacelike; in particular, the little known geodesics of simultaneities. We also study the non-geodetic circular…
We consider diagonal cylindrically symmetric metrics, with an interior representing a general non-rotating fluid with anisotropic pressures. An exterior vacuum Einstein-Rosen spacetime is matched to this using Darmois matching conditions.…
We investigate the geodesics in the entire class of nonexpanding impulsive gravitational waves propagating in an (anti-)de Sitter universe using the distributional form of the metric. Employing a 5-dimensional embedding formalism and a…
In this paper, we establish a sufficient condition for a geodesic in a Riemannian manifold to be homogeneous, i.e. an orbit of an $1$-parameter isometry group. As an application of this result, we provide a new proof of the fact that every…
In this article, we look into geodesics in the Schwarzschild-Anti-de Sitter metric in (3+1) spacetime dimensions. We investigate the class of marginally bound geodesics (timelike and null), while comparing their behavior with the normal…
We consider spacetimes consisting of a manifold with Lorentzian metric and a weight function or scalar field. These spacetimes admit a Bakry-\'Emery-Ricci tensor which is a natural generalization of the Ricci tensor. We impose an energy…
We prove the nonlinear stability of the cosmological region of Kerr de Sitter spacetimes. More precisely, we show that solutions to the Einstein vacuum equations with positive cosmological constant arising from data on a cylinder that is…
The global time in Geometrodynamics is defined in a covariant under diffeomorphisms form. An arbitrary static background metric is taken in the tangent space. The global intrinsic time is identified with the mean value of the logarithm of…