This is as well true about the generally covariant geodesic equation.
According to the scalar geodesic equation (equation of energy), two factors, [F.
The geodesic equation
becomes non-inertial forces as a result of the variation in the local index of refraction and motion the tetrad field represents.
where m is the (rest) mass, e is the electric charge, and c is the speed of light in vacuum, such that the physical fields are intrinsic to the space-time geometry itself, as manifest in generalized geodesic equation
of motion [Du.
Motion of the particles is determined by the well-known geodesic equation
cb] = 0 to generate the necessary geodesic equation
Thus, the displacement from a fixed object induced by gravitational wave, according the geodesic equation
, has nothing to do with the distance between them (see Section 2).
7) to (9) imply that not only the geodesic equation
, the Lorentz gauge, but also Maxwell's equation are satisfied.
The dipole anisotropy, which is due to the rapid motion of the source (the Earth) in the weak intergalactic field, is analysed by using the geodesic equations
for light-like particles (photons), which are mediators for electromagnetic radiation.
whose Euler-Lagrange equations are the geodesic equations
If considering a free test-body constrained to move only along only the Earth's gravitational field-lines (falling freely in the z-direction), such an additional force is expressed in the geodesic equation
along the z-direction (62)
In General Relativity, the change of the energy of a freely moving photon should be the solution to the scalar equation of the isotropic geodesic equations
, which manifests the work produced on the photon being moved along the path.
alpha]] = 0), they move along neighbouring geodesic lines, according to the geodesic equations
Thus relative accelerations of free test-particles are caused by the presence the space curvature [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], and linear velocities of the particles are determined by the geodesic equations
The equations of motion of free particles are the geodesic equations