normal acceleration) to the geodesic equation
(9) for a unit speed robot to follow the path [[gamma].
The geodesic equation
then becomes changing speed due to an index of refraction, bending due to Huygens' principle and frame dragging due to advection.
By solving the scalar geodesic equation
for a mass-bearing particle ("stone-like objects"), we shall obtain that the relativistic mass of the object changes according to the remoteness to the observer in the particular space.
Here we are interested in the derivation of the generalized geodesic equation
of motion such that our geodesic paths correspond to the formal solution of the quantum gravitational wave equation in the preceding section.
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)
z]) = 0, formula (6) does produces a geodesic equation
From the geodesic equation
, clearly it is impossible to justify (7) for any frame of reference.
cb] = 0 to generate the necessary geodesic equation
which is different from the geodesic equation
in that the right part in not zero here.
In order to study the motion of planets and light rays in a homogeneous time varying spherical spacetime, there is need to derive the geodesic equations
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.
The second problem is solved using the geodesic equations
for light-like particles (photons) which are mediators for electro-magnetic radiation.
alpha]] = 0), they move along neighbouring geodesic lines, according to the geodesic equations