The Resultant Red-Shift of a Source in the Case of the Merger of the Schwarzschild Space-Time with the Flat Robertson-Walker Space-Time

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.