Browsing by Author "Senevirathne, K.W.P.B."

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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
(University of Kelaniya, 2007) Senevirathne, K.W.P.B.; de Silva, L.N.K.
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.
The Sehwarzschild Space-Time in the Background of the Flat Robertson-Walker Space-Time
(University of Kelaniya, 2007) Senevirathne, K.W.P.B.; de Silva, L.N.K.
The Schwarzschild space-time is well known in describing the gravitational field of an object in an otherwise empty universe. The Schwarzschild space-time was derived by Karl Schwarzschild ( 1916) considering the merger of the Schwarzschild space-time with the Lorentz metric as the boundary (!)_ However, the Loremtz metric cannot be used in investigations of non empty large scale space-times, the whole universe being one such case. Thus, the cosmologists use the Robertson-Walker space-times, in describing the universe (2. -'i. As a result it becomes necessary to investigate the gravitational field of an object in the background of the Robertson-Walker space-time, We have studied the merger of the isotropic Schwarzschild space-time with the flat Robertson-Walker space-time. In this scenario, the flat Robertson-Walker space-time was considered for simplicity. The expressions for the radial coordinates r11 and rJl at the merger of the flat Robertson-Walker space-time and the isotropic Schwarzschild space-time were derived in terms of the scale factor R(t) and a constant R* and found to be given by An analytic expression for the time coordinate ( t) of the Schwarzschild space-time was obtained in the case of the de-Sitter universe, l = 2T0 In[- 1 !R' _l where To is the reciprocal of the Hubble constant (2'. 2~ I( - Jf?(t) J Schwarzschild Flat Robertson-Walker space-time space-time Figure: The radial coordinates and the time coordinates of the Schwarzschild space-time and the t1at Robertson Walker space-time at the merger The derived expressions for the radial coordinates '~, and rJI imply that an object in the universe begins to communicate with the "outside world" after a particular time, before which r11 and rfl are negative. At this particular time, R(t) approaches the constant R* and r,, , rfl tend to infinity. It could be said that the object comes into existence as far as the rest of the universe is concerned at this particular instant. The values of r11 and rf.i decrease with increase of time. When the time coordinate of the Schwarzschild space-time tends to infinity, rfl achieves the value (;) , the value of the Schwarzschild radius in isotropic coordinates.