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We examine relativistic diffusion through the frame and observer bundles associated with a Lorentzian manifold $(M,g)$. Our focus is on spacetimes with a non-trivial isometry group, and we detail the conditions required to find symmetric…
All Lorentzian spacetimes with vanishing invariants constructed from the Riemann tensor and its covariant derivatives are determined. A subclass of the Kundt spacetimes results and we display the corresponding metrics in local coordinates.…
Effective estimates for the lattice point discrepancy of certain planar and three-dimensional domains. This paper provides estimates, with explicit constants, for the lattice point discrepancy of o-symmetric ellipse discs and ellipsoids in…
In this paper we investigate the statistical properties of gravitational lenses for models in which a cosmological term decreases with time as $\Lambda \propto a^{-m}$, where $a$ is the scale factor and $m$ is a parameter ($0 \leq m < 3$).…
The $ \gamma $-spacetime metric is a static and axially symmetric vacuum solution of the Einstein equation. This spacetime represents a naked singularity and it has an extra parameter $ \gamma $ which signifies deviations from spherical…
Lie derivatives of various geometrical and physical quantities define symmetries and conformal symmetries in general relativity. Thus we obtain motions, collineations, conformal motions and conformal collineations. These symmetries are used…
In a previous article concerning image distortion in non-perturbative gravitational lensing theory we described how to introduce shape and distortion parameters for small sources. We also showed how they could be expressed in terms of the…
Gravitational waves cause freely falling spinning objects to precess, resulting in a net orientation change called gyroscopic memory. In this paper, we will consider isolated gravitational sources in the post-Newtonian framework and compute…
For known gravitational lens systems the redshift distribution of the lenses is compared with theoretical expectations for $10^{4}$~Friedmann-Lema\^\i tre~cosmological models, which more than cover the range of possible cases. The…
The description of an observer's measurement in general relativity and the standard model of particle physics is closely related to the spacetime metric. In order to understand and interpret measurements, which test the metric structure of…
We provide physical interpretation for the four parameters of the stationary Lewis metric restricted to the Weyl class. Matching this spacetime to a completely anisotropic, rigidly rotating, fluid cilinder, we obtain from the junction…
We present a useful method for the construction of cosmological models by solving the differential equations arising from calculating the kinematical invariants (shear, rotation, expansion and acceleration) of an observer field in proper…
This work studies the periapsis shift in the equatorial plane of arbitrary stationary and axisymmetric spacetimes. Two perturbative methods are systematically developed. The first work for small eccentricity but very general orbit size and…
A general form of a metric preserving all symmetries of a spherically symmetric gravitational field and angular momentum in spherical coordinates is obtained. Such metric may have $g_{01}(r)\neq 0$. The Newtonian limit uniquely defines…
Gravitational lensing constitutes one of the most direct observational manifestations of spacetime curvature and provides a powerful probe of compact astrophysical objects. In this work, we present a comprehensive analysis of the bending of…
It is shown that in general relativity some static metrics are able to simulate oscillatory motions. Their form depends on two arbitrary real parameters which determine the specific oscillation modes. The conclusion is that these metrics…
Gravitational lensing by rotating extended deflectors is discussed. Due to spin, corrections on image positions, caustics and critical curves can be significant. In order to obtain realistic quantitative estimates, the lens is modeled as a…
The geodesic deviation equation (`GDE') provides an elegant tool to investigate the timelike, null and spacelike structure of spacetime geometries. Here we employ the GDE to review these structures within the…
The orbital Lense-Thirring precession is considered in the context of constraints for weak-field General Relativity involving the cosmological constant $\Lambda$. It is shown that according to the current accuracy of satellite measurements…
A subclassification of stationary spacetimes, endowed with one timelike and one spacelike Killing vectors, i.e., Petrov $G{_2}I$ on $T_2$ spaces, is proposed. Special attention deserves the Collison's theorem [1] and the branch of metrics…