Analysis of the null geodesics in Schwarzschild de-Sitter space-time

The gravitational field of a spherically symmetric mass in a universe with cosmological constant (Λ) is described in terms of Schwarzschild de-Sitter (SdS) space-time. Based on this space-time we investigated the geodesics of a test particle-photon. We performed our study on the space-time in between the cosmological event horizon and black hole event horizon i.e. r_H < r < r_C and also imposed E² > V_eff for the physical acceptance. We detected two types of orbits, namely periodic bound orbit and terminating bound orbit. The mathematical conditions for the existence of these orbits have been discussed. We found that there will no longer be any periodic bound orbits for a large positive cosmological constant. The analysis of effective potential inferred us that only the peak of the curve changes for change in angular momentum (L). These peaks correspond to circular orbits in null geodesics and a circular orbit of radius 3M becomes an allowed null geodesic. (author)