相关论文: Bilocal geodesic operators in static spherically-s…

We analyze a variational time discretization of geodesic calculus on finite- and certain classes of infinite-dimensional Riemannian manifolds. We investigate the fundamental properties of discrete geodesics, the associated discrete…

In this paper we study Strichartz estimates for dispersive equations which are defined by radially symmetric pseudo-differential operators, and of which initial data belongs to spaces of Sobolev type defined in spherical coordinates. We…

The Einstein equations for spacetimes with two commuting spacelike Killing field symmetries are studied from a Hamiltonian point of view. The complexified Ashtekar canonical variables are used, and the symmetry reduction is performed…

The transport of charged particles or photons in a scattering medium can be modelled with a Boltzmann equation. The mathematical treatment for scattering in such scenarios is often simplified if evaluated in a frame where the scattering…

Given the extreme accuracy reached by future global space astrometry, one needs a global relativistic modeling of observations. A relativistic definition of astrometric observables is then essential to find uniquely coordinates, parallax…

We derive an explicit formula for the Laplace-Beltrami operator on the orthogonal Stiefel manifold, viewed as a constraint submanifold of the Euclidean space of real matrices equipped with the Frobenius metric. Using the general framework…

In this research note we introduce a new approximation of photon geodesics in Schwarzschild spacetime which is especially useful to describe highly bent trajectories, for which the angle between the initial emission position and the line of…

We use the Hamiltonian formulation of the geodesic equation in the Schwarzschild space-time so as to get the variational equation as the counterpart of the Jacobi equation in this approach. In this context we are able to apply the…

For a general spherically four--dimensional metric the notion of "circularity" of a family of equatorial geodesic trajectories is defined in geometrical terms. The main object turns out to be the angular--momentum function $J$ obeying a…

The geodesics in various spherical Rindler frames are investigated. A display of some kinematical quantities of the spacetime is given. The constant acceleration from the metric acts as the surface gravity of the horizon $r = 0$. The radial…

The direct geodesic problem on an oblate spheroid is described as an initial value problem and is solved numerically in geodetic and Cartesian coordinates. The geodesic equations are formulated by means of the theory of differential…

The geodesics on the $(1+3)$-dimensional de Sitter spacetime are considered studying how their parameters are determined by the conserved quantities in the conformal Euclidean, Friedmann-Lema\^itre-Robertson-Walker, de Sitter-Painlev\'e and…

Starting with an exact and simple geodesic, we generate approximate geodesics by summing up higher-order geodesic deviations within a General Relativistic setting, without using Newtonian and post-Newtonian approximations. We apply this…

The time dependent conformally-flat spherical Rindler spacetime is investigated. The geometry has an apparent horizon that coincides with the causal horizon. The scalar acceleration of a static observer is constant and equals to the…

Equations of geodesic deviation for the 3-dimensional and 4-dimensional Riemann spaces are discussed. Availability of wide classes of exact solutions of such equations, due to recent results for the matrix Schr\"odinger equation, is…

We present formal expressions for the optical scalars in terms of the curvature scalars in the weak gravitational lensing regime at second order in perturbations of a flat background without mentioning the extension of the lens or their…

The complete analytical solutions of the geodesic equation of massive test particles in higher dimensional Schwarzschild, Schwarzschild-(anti)de Sitter, Reissner-Nordstroem and Reissner-Nordstroem-(anti)de Sitter space--times are presented.…

We investigate the wave optics in spherically symmetric spacetimes: Schwarzschild black hole, spherical star with a perfect absorbing surface, and massless/massive Ellis wormholes. Assuming a point wave source, wave pattern and power…

We investigate a relativistic positioning system where the coordinates of the users are determined by the proper times broadcasted by clocks in motion in spacetime: these are the so-called emission coordinates. In particular, we focus on…

Approximate symmetries of geodesic equations on 2-spheres are studied. These are the symmetries of the perturbed geodesic equations which represent approximate path of a particle rather than exact path. After giving the exact symmetries of…