Dynamical system scenario for accretion discs: Dark energy acting through the spacetime metric

Studies of accretion toward black holes are found in the literature where dark energy is chosen to act as the accreting agent. Studies of a dynamical system related to such a phase portrait are also available. In this paper, the central engine is opted to be embedded in a dark energy universe. Footprints of the dark energy equation of state are found in the black hole’s metric chosen by us. Using the pseudo Newtonian method, the force complexity due to relativity is replaced with simplified terms. Dynamical system for a viscous accretion is constructed. Each point of this said system is a three-coordinated tuple presenting radial inward speed, sonic speed and specific angular momenta one after the other. A bent curve of center equilibrium is found. Two planes are seen which are, respectively, attractor and repeller. Every case is physically interpreted. For a viscous accretion onto a dark energy embedded black hole, it is followed that the center equilibrium points are forming a closed curve taking the origin on its own plane. Though the orbit of such a center equilibrium curve keeps only a part of it in the space of discussion.