Geodesics Structure and Light Deflection of Regular Phantom Black Hole

The geodesic structure of Regular Phantom Black Holes ($\mathbf{\text{RPBH}}$) space–time is analyzed and discussed in three asymptotically cases: Flat, de Sitter ($\mathbf{\text{dS}}$), and Anti–de Sitter ($\mathbf{\text{AdS}}$). The impact of the important scale parameter $b$\footnote{This parameter determines the coupling strength between phantom field and gravity.} on the trajectory of particles is studied and investigated which can mimic repulsion or attraction. By virtue of Effective Potential ($\mathbf{\text{EP}}$) tool, the circular orbits and their stability are discussed. Also, in the asymptotically flat spacetime, the angle of light deflection versus the scale parameter is presented.