Related papers: On geodesic deviation in Schwarzschild spacetime
In general relativity, an external observer cannot distinguish distinct internal structures between two spherically symmetric stars that have the same total mass $M$. However, when quantum corrections are taken into account, the external…
The Schwarzschild geometry is investigated within the context of effective-field-theory models of gravity. Starting from its harmonic-coordinate expression, we derive the metric in standard coordinates by keeping the leading one-loop…
We study the geodesic motion in a space-time describing a swirling universe. We show that the geodesic equations can be fully decoupled in the Hamilton-Jacobi formalism leading to an additional constant of motion. The analytical solutions…
For the Bianchi type VI universe, exact solutions of the equation of geodesic deviation in a strong primordial gravitational wave in a privileged coordinate system are obtained. The solutions refer to Shapovalov's gravitational-wave models…
We consider geodesics of massive and massless test particles in the gravitational field of a static and axisymmetric compact object described by the quadrupolar metric ($q$-metric), which is the simplest generalization of the Schwarzschild…
We consider a system of nonlinear wave equations with constraints that arises from the Einstein equations of general relativity and describes the geometry of the so-called Gowdy symmetric spacetimes on T3. We introduce two numerical…
The general relativistic gravitomagnetic clock effect consists in the fact that two massive test bodies orbiting a central spinning mass in its equatorial plane along two identical circular trajectories, but in opposite directions, take…
Geometric optics effectively describes the propagation of electromagnetic waves when the wavelength is much smaller than the characteristic length scale of the medium, making wave phenomena like diffraction negligible. As a result, light…
We consider a traversable wormhole solution of Einstein's gravity conformally coupled to a massless scalar field, a solution derived by Barcelo and Visser based on the JNWW spacetime. We study the geodesic motion of time-, light- and…
We study the geodesic motion of test particles in the space-time of non-compact boson stars. These objects are made of a self-interacting scalar field and -- depending on the scalar field's mass -- can be as dense as neutron stars or even…
Gravitational radiation of binary systems can be studied by using the adiabatic approximation in General Relativity. In this approach a small astrophysical object follows a trajectory consisting of a chained series of bounded geodesics…
The motion of satellite constellations similar to GPS and Galileo is numerically simulated and, then, the region where bifurcation (double positioning) occurs is appropriately represented. In the cases of double positioning, the true…
We consider the motion of test particles in the spacetime of a black hole in f(R) gravity. The complete set of analytic solutions of the geodesic equation in the spacetime of this black hole are presented. The geodesic equations are solved…
The Gibbons-Werner method for the gravitational deflection angle of unbound particles in static spherically symmetric spacetimes is based on Jacobi metric and Gauss-Bonnet theorem. When it is extended to bound massive particles, there…
In this paper we derive the leading quantum gravitational corrections to the geodesics and the equations of motion for a scalar field in the spacetime containing a constant density star. It is shown that these corrections can be calculated…
General Relativity (GR) is shown to be a complete theory with respect to the isochrony of the pendulum. This guarantees that time can be measured with a mechanical clock within the theory itself as a matter of principle. The proper and…
Set of analytic solutions of the geodesic equation in a spherical conformal spacetime is presented. Solutions of this geodesics can be expressed in terms of the Weierstrass {\wp} function and the Kleinian {\sigma} function. Using conserved…
We study geodesic motion in expanding spherical impulsive gravitational waves propagating in a Minkowski background. Employing the continuous form of the metric we find and examine a large family of geometrically preferred geodesics. For…
The discovery of the accelerating expansion of the Universe, thought to be driven by a mysterious form of `dark energy' constituting most of the Universe, has further revived the interest in testing Einstein's theory of General Relativity.…
Based on the Generalized Principle of Inertia, which states that: \emph{An inanimate object moves freely, that is, with zero acceleration, in its own spacetime, whose geometry is determined by all of the forces affecting it,} we geometrize…