Epicyclic frequencies and stability of thin shell around the traversable phantom wormholes in Rastall gravity

In this study, we calculate the wormhole solutions with the phantom regime via the conformal symmetry in the background of Rastall gravity. The current analysis also explores the physical aspects of the epicyclic frequencies. In the astrophysical epicyclic frequencies are widely used to explore the self-gravitating system. The exact shape function is calculated by using the equation of state. All the energy conditions are checked for the estimated shape function with the phantom regime. The developed structure of traversable phantom wormhole is further investigated by using a black hole geometry as an exterior manifold surrounded by perfect fluid in Rastall gravity. The different types of matter distribution around black hole geometry such as quintessence, cosmological constant and phantom energy are considered to discuss stable as well as physical characteristics of the shell. The speed of sound parameter is used to explore the stable configuration of the shell around a traversable phantom wormhole geometry. Rastall parameter greatly affects the physical features of the shell such as proper length, entropy and shell energy. It is interesting to mention that there is a linear relationship among proper length, entropy, shell energy and thickness of the shell.