相关论文: Bilocal geodesic operators in static spherically-s…
For metrology, geodesy and gravimetry in space, satellite based instruments and measurement techniques are used and the orbits of the satellites as well as possible deviations between nearby ones are of central interest. The measurement of…
Several physical problems such as the `twin paradox' in curved spacetimes have purely geometrical nature and may be reduced to studying properties of bundles of timelike geodesics. The paper is a general introduction to systematic…
Realistic modelling of radiation transfer in and from variable accretion disks around black holes requires the solution of the problem: find the constants of motion and equation of motion of a light-like geodesic connecting two arbitrary…
Propagation of light in nonlinear materials is here studied in the regime of the geometrical optics. It is shown that a spherically symmetric medium at rest with some specific dielectric properties can be used to produce an exact analogue…
We lay out a general framework for calculating the variation of a set of cosmological observables, down the past null cone of an arbitrarily placed observer, in a given arbitrary inhomogeneous metric. The observables include redshift,…
We introduce an exactly solvable example of timelike geodesic motion and geodesic deviation in the background geometry of a well-known two-dimensional black hole spacetime. The effective potential for geodesic motion turns out to be either…
In this paper, we study the geodesic motion in spherically symmetric electro-vacuum Euclidean solutions of the Einstein equation. There are two kinds of such solutions: the Euclidean Reissner-Nordstr\"{o}m (ERN) metrics, and the…
We introduce in the explicit form the tetrads of arbitrary observers in spacetimes with spherical and axial symmetries. The observers confined to the equatorial plane are parametrized by the pair of functions. We apply this description in…
We construct a one-parameter family of static and spherically symmetric solutions to the Einstein-Vlasov system bifurcating from the Schwarzschild spacetime. The constructed solutions have the property that the spatial support of the matter…
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…
This is a consecutive paper on the timelike geodesic structure of static spherically symmetric spacetimes. First we show that for a stable circular orbit (if it exists) in any of these spacetimes all the infinitesimally close to it timelike…
We present a framework for studying gravitational lensing in spherically symmetric spacetimes using 1+1+2 covariant methods. A general formula for the deflection angle is derived and we show how this can be used to recover the standard…
We investigate geodesic orbits and manifolds for metrics associated with Schwarzschild geometry, considering space and time curvatures separately. For `a-temporal' space, we solve a central geodesic orbit equation in terms of elliptic…
We solve the geodesic deviation equations for the orbital motions in the Schwarzschild metric which are close to a circular orbit. It turns out that in this particular case the equations reduce to a linear system, which after…
The timelike geodesic equations resulting from the Kerr gravitational metric element are derived and solved exactly including the contribution from the cosmological constant. The geodesic equations are derived, by solving the…
We present a space-time multiscale method for a parabolic model problem with an underlying coefficient that may be highly oscillatory with respect to both the spatial and the temporal variables. The method is based on the framework of the…
The starting point of this work is the principle that all movement of particles and photons in the observable Universe must follow geodesics of a 4-dimensional space where time intervals are always a measure of geodesic arc lengths, i.e.…
The Kottler spacetime in isotropic coordinates is known where the metric is time-dependent. In this paper, the Kottler spacetime is given in isotropic static coordinates (i.e., the metric components are time-independent). The metric is…
We analyze the behaviour of geodesic motion of test particles in the spacetime of a specific class of axially symmetric static vacuum solutions to the Einstein equations, hereafter referred to as linearized multipole solution (LM). We…
The coefficient function of the leading differential operator is estimated from observations of a linear stochastic partial differential equation (SPDE). The estimation is based on continuous time observations which are localised in space.…