Let us consider two neighboring geodesic paths [[theta].sup.[alpha]]([tau]) and [[theta].sup.[alpha]]([tau]) + [delta][[theta].sup.[alpha]]([tau]), with [tau] denoting the affine parameter, that satisfy the following

geodesic equations of motion:

For the

geodesic equation in this notation we have [F.sup.i] = - [[GAMMA].sup.i.sub.[mu]v]([v.sup.[mu]][v.sup.v]/([c.sup.2]-v[gamma]v)).

In two recent papers [4, 5], I solved the scalar

geodesic equation for mass-bearing particles and massless particles (photons), in the most studied particular spaces: in the space of Schwarzschild's mass-point metric, in the space of an electrically charged mass-point (the Reissner-Nordstrom metric), in the rotating space of Godel's metric (a homogeneous distribution of ideal liquid and physical vacuum), in the space of a sphere of incompressible liquid (Schwarzschild's metric), in the space of a sphere filled with physical vacuum (de Sitter's metric), and in the deforming space of Friedmann's metric (empty or filled with ideal liquid and physical vacuum).

The second problem was solved using the

geodesic equations for light-like particles (photons) which are mediators for electromagnetic radiation.

whose Euler-Lagrange equations are the

geodesic equations* We should also add that, coming from the

geodesic equation along the z-axis, which is the third equation of (61), to the simplified form (62) thereof, we omitted the harmonic term from consideration.

If a

geodesic equation must be produced, for a monochromatic wave with frequency w, the form of a photonic energy tensor should be similar to that of massive matter.

From the

geodesic equation, clearly it is impossible to justify (7) for any frame of reference.

(3) allows [[nabla].sup.c] T[(L).sub.cb] = 0 to generate the necessary

geodesic equation for photons.

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 [2].

Among the most relevant DEs are the

geodesic equations