The Three Paths of Light

A light ray motions from A to B in a gravitational field.
After some consideration, three different paths describe the same path:
The First Path: This is the longest. If you take the local scale for each point the ray passes through, the path can be longer than the radius of the star. Local distances can be calculated using the reciprocal of the scale change (example). It is also possible to apply the Schwarzschild metric with the snow globe potential. This path is the longest to the maximum length scale. Starting from the small radius with the local scale, it can even be shorter than the Euclidean distance.
The Second Path: This path is relative to a point. Using the (relative) scale changes of the "snow globe theorie", you obtain relative refractive indices and can thus be calculated. Once you have this path to the maximum (length) scale, you also have the first path. The length of the first path is obtained by taking the path integral of the second path and taking the reciprocal of the space reduction.
The Third Way: In order to observe the location points, the narrowing of the view cone must also be taken into account. Using the method for the second path, the initial angle can be determined. The narrowing of the view cone is a purely optical effect. Due to the magnification, it is difficult to determine velocities by sight. However, it is possible to obtain proper time from the redshift, since in the "snow globe theory" Kepler's laws apply locally.
Such paths also exist for massive objects, such as those in the Einstein elevator.
Note:
Cosmological measurements only provide images from a distance. Changes in scale also occur in optical images. Using the redshift, objects can be connected to their "proper time".
Question: If the light path is longer than the Euclidean path, what about the conservation of energy?
As we know, energy is force times distance. In the Einstein elevator, the Newtonian potential -G•M/R was used. The starting point is the point with the maximum length scale. From this point, the mass appears as a"ghost mass". Thus, the energies for both paths are the same.

Ludwig Resch