Abstract:
The red-shift of a source in the space can be described by considering the Schwarzschild
space-time (I) (gravitational red-shift) or the Robertson-Walker space-time (2)
(cosmological red-shift). When obtaining expressions for the red-shift, the path of light
particles or photons plays an important role (3l. In the case of merger of the isotropic
Schwarzschild space-time with the flat Robertson-Walker space-time, it is not
meaningful to discuss the path of light particles or photons in the isotropic Schwarzschild
space-time or the flat Robertson-Walker space-time separately.
We have considered the red-shift of a source as observed by an observer on the other side
of the merger. The expressions for the radial coordinates, derived by the authors (4l, at the
merger of the isotropic Schwarzschild space-time and the flat Robertson-Walker spacetime
were used.
Schwarzschild
space-time
Path of the photon
Robertson-Walker
space-time
Path of the photon
Photon
Figure: Radial motion of a photon with the source in the flat Robertson-Walker space-time
When the source is located in the flat Robertson-Walker space-time, the observer is
considered to be in the isotropic Schwarzschild space-time and vise versa. The
expressions for the gravitational red-shift and the cosmological red-shift of the source
were derived, and the resultant red-shift of the source was obtained from these
expressions.
