相关论文: Nonrelativistic Geodesic Motion

A new, second-order solution in curvilinear coordinates is introduced for the relative motion of two spacecraft on eccentric orbits. The second-order equations for unperturbed orbits are derived in spherical coordinates with true anomaly as…

Relativistic thermodynamics is treated from the point of view of kinetic theory. It is shown that the generalized J\"uttner distribution suggested in [1] is compatible with kinetic equilibrium. The requirement of compatibility of kinetic…

We present an overview of recent developments in the numerical solution of Horndeski gravity theories, which are the class of all scalar-tensor theories of gravity that have second order equations of motion. We review several methods that…

With the aid of a Fermi-Walker chart associated with an orthonormal frame attached to a time-like curve in spacetime, a discussion is given of relativistic balance laws that may be used to construct models of massive particles with spin,…

In the context of general relativity, the geodesic deviation equation (GDE) relates the Riemann curvature tensor to the relative acceleration of two neighboring geodesics. In this paper, we consider the GDE for the generalized hybrid…

Given two points of a Generalized Robertson-Walker spacetime, the existence, multiplicity and causal character of geodesic connecting them is characterized. Conjugate points of such geodesics are related to conjugate points of geodesics on…

We introduce a model of noncommutative geometry that gives rise to the uncertainty relations recently derived from the discussion of a quantum clock. We investigate the dynamics of a free particle in this model from the point of view of…

We consider alternative theories of gravity with a direct coupling between matter and the Ricci scalar We study the relation between these theories and ordinary scalar-tensor gravity, or scalar-tensor theories which include non-standard…

The motion of spinning relativistic particles in external electromagnetic and gravitational fields is considered. A simple derivation of the spin interaction with gravitational field is presented. The self-consistent description of the spin…

In this paper, we investigate gravitational waves beyond the linear approximation, focusing on second-order contributions sourced by linearized waves in the transverse-traceless (TT) gauge. A general spacetime metric is constructed, and…

We consider the path space of a curved manifold on which a point particle is introduced in a conservative physical system with constant total energy to formulate its action functional and geodesic equation together with breaks on the path.…

In special-relativistic physics, spacetime is imbued with a fixed, non-dynamical metric tensor. A path to gravitational theory is to promote this tensor to a genuine dynamical field. An alternative description of special-relativistic…

The semidirect product of the real Heisenberg group ${\rm H}_1(\mathbb{R})$ with ${\rm SL}(2,\mathbb{R})$, called the real Jacobi group $G^J_1(\mathbb{R})$, admits a four-parameter invariant metric expressed in the S-coordinates. We…

An analysis of composite inertial motion (relativistic sum) within the framework of special relativity leads to the conclusion that every translational motion must be the symmetrically composite relativistic sum of a finite number of quanta…

The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic…

Using dimensional analysis techniques we present an extension of Newton's gravitational theory built under the assumption that Milgrom's acceleration constant is a fundamental quantity of nature. The gravitational force converges to…

A new formulation of relativistic quantum mechanics is proposed in the framework of the rest-frame instant form of dynamics with its instantaneous Wigner 3-spaces and with its description of the particle world-lines by means of derived…

The geodesic properties of the extraordinary vacuum string solution in (4+1) dimensions are analyzed by using Hamilton-Jacobi method. The geodesic motions show distinct properties from those of the static one. Especially, any freely falling…

Sasakian manifolds provide explicit formulae of some Jacobi operators which describe the biharmonic equation of curves in Riemannian manifolds. In this paper we characterize non-geodesic biharmonic curves in Sasakian manifolds which are…

In arXiv:1904.12869 it was shown how in an adiabatic limit the vacuum Einstein equations on a compact spatial region can be re-expressed as geodesic equations on the group of diffeomorphisms of the boundary. This is reminiscent of the…