Related papers: All relativistic motions can be geodesically descr…
A relativistic self-gravitating equilibrium system with steady flow as well as spherical symmetry is discovered. The energy-momentum tensor contains the contribution of a current related to the flow and the metric tensor does an…
Relativity is an integral part of positioning systems, and this is taken into account in today's practice by applying many "relativistic corrections" to computations performed using concepts borrowed from Galilean physics. A different,…
There is proven a theorem, to the effect that a material body in general relativity, in a certain limit of sufficiently small size and mass, moves along a geodesic.
A special form of the isotropic metric in cylindrical coordinates is used to construct what may be interpreted as the General Relativistic versions of some wellknown potential-density pairs used in Newtonian gravity to model…
Geometric models of quantum relativistic rotating oscillators in arbitrary dimensions are defined on backgrounds with deformed anti-de Sitter metrics. It is shown that these models are analytically solvable, deriving the formulas of the…
The metric tensor field equations for the general quadratic curvature gravity in four spacetime dimensions are derived by making use of the algebra of the exterior forms defined on pseudo-Riemannian manifolds and the identities satisfied by…
We show that a three rank Lanczos type tensor field is an appropriate choice to describe relativistic electromagnetic and gravitational effects. More precisely, we identify the irreducible field-decompositions of this tensor as…
The gravitational field of a particle of small mass $\mu$ moving through curved spacetime, with metric $g_{ab}$, is naturally and easily decomposed into two parts each of which satisfies the perturbed Einstein equations through $O(\mu)$.…
According to General Relativity, as distinct from Newtonian gravity, motion under gravity is treated by a theory that deals, initially, only with test particles. At the same time, satellite measurements deal with extended bodies. We discuss…
The (4+1) dimensional conformally flat Eisenhart geometry is investigated in this work, stressing the contribution of the stress tensor generating its curvature. The energy-momentum tensor $T^{a}_{~b}$ is traceless and has only one nonzero…
The geometrical nature of gravity emerges from the universality dictated by the equivalence principle. In the usual formulation of General Relativity, the geometrisation of the gravitational interaction is performed in terms of the…
Inertia has long been treated as the paradigm of natural motion. This paper challenges this identification through the lens of General Relativity. Drawing on Norton (2012)'s distinction between idealisation and approximation and analysing…
General relativity can be presented in terms of other geometries besides Riemannian. In particular, teleparallel geometry (i.e., curvature vanishes) has some advantages, especially concerning energy-momentum localization and its…
Relativistic mechanics on an arbitrary manifold is formulated in the terms of jets of its one-dimensional submanifolds. A generic relativistic Lagrangian is constructed. Relativistic mechanics on a pseudo-Riemannian manifold is particularly…
In the general relativity theory the basic ingredient to describe gravity is the geometry, which interacts with all forms of matter and energy, and as such, the metric could be interpreted as a true physical quantity. However the metric is…
In considering the mathematical problem of describing the geodesics on a torus or any other surface of revolution, there is a tremendous advantage in conceptual understanding that derives from taking the point of view of a physicist by…
An explicit expression for the Jacobi metric for a general Lagrangian system is obtained as a series expansion in the square root of the kinetic energy of the system and the corresponding geodesics are described in terms of an appropriate…
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…
The motion of sufficiently small body in general relativity should be accurately described by a geodesic. However, there should be ``gravitational self-force'' corrections to geodesic motion, analogous to the ``radiation reaction forces''…
We show that the gravitational field equations derived from an action composed of i) an arbitrary function of the scalar curvature and other scalar fields plus ii) connection-independent kinetic and source terms, are identical whether one…