Related papers: Separable geodesic action slicing in stationary sp…
We derive general conditions under which geodesics of stationary spacetimes resemble trajectories of charged particles in an electromagnetic field. For large curvatures (analogous to strong magnetic fields), the quantum mechanicical states…
In the present paper we study the geodesic motion of test particles and light rays in the spacetime of a static charged black hole in $f(R)$ gravity. The complete set of analytic solutions of the geodesic equations in the spacetime of this…
In this article we study the geodesic motion of test particles and light in the five-dimensional (rotating) black string spacetime. If a compact dimension is added to the four-dimensional Schwarzschild or Kerr spacetime, the new…
The influence of spin on a photon's motion in a Schwarzschild and FRW spacetimes is studied. The first order correction to the geodesic motion is found. It is shown that unlike the world-lines of spinless particles, the photons world-lines…
We give a precise theoretical description of initially aligned sets of orthogonal gyroscopes which are transported along different paths from some initial point to the same final point in spacetime. These gyroscope systems can be used to…
The advent of data science has provided an increasing number of challenges with high data complexity. This paper addresses the challenge of space-time data where the spatial domain is not a planar surface, a sphere, or a linear network, but…
A region-delimited gravitational wave field can be constructed, such that a subset of geodesics crossing this region will move faster than nearby geodesics moving entirely inside flat spacetime, along a preferred direction. Null geodesics…
The standard Lense-Thirring metric is a century-old slow-rotation large-distance approximation to the gravitational field outside a rotating massive body, depending only on the total mass and angular momentum of the source. Although it is…
Lensing in a spherically symmetric and static spacetime is considered, based on the lightlike geodesic equation without approximations. After fixing two radius values r_O and r_S, lensing for an observation event somewhere at r_O and static…
The explicit relationship is determined between the interior properties of a static cylindrical matter distribution and the metric of the exterior space-time according to Einstein gravity for space-time dimensionality larger or equal to…
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…
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…
The gravitational collapse of a spherical distribution, in a class of f(R) theories of gravity, where f(R) is power function of R, is discussed. The spacetime is assumed to admit a homothetic Killing vector. In the collapsing modes, some of…
For any configuration of a static plane-symmetric distribution of matter along space-time, there are coordinates where the metric can be put explicitly as a functional of the energy density and pressures. It satisfies Einstein equations as…
We present a generalized Newtonian description of particle dynamics valid for any spherically symmetric, static black hole spacetime. This approach is derived from the geodesic motion of test particles in the low-energy limit. It reproduces…
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…
We investigate the fully general class of non-expanding, non-twisting and shear-free D-dimensional geometries using the invariant form of geodesic deviation equation which describes the relative motion of free test particles. We show that…
It is shown that properties of a discrete space-time geometry distinguish from properties of the Riemannian space-time geometry. The discrete geometry is a physical geometry, which is described completely by the world function. The discrete…
The precession angular velocity of a gyroscope moving along a general geodesic in the Kerr spacetime is analyzed using the geometric properties of the spacetime. Natural frames along the gyroscope world line are explicitly constructed by…
In general relativity, the motion of an extended body moving in a given spacetime can be described by a particle on a (generally non-geodesic) worldline. In first approximation, this worldline is a geodesic of the underlying spacetime, and…