History of a Particle Bounded to the Cosmological LTB Black Hole Surrounded by the Quintom Field

This paper provides a complete set of analytic time-varying geodesic equations of the LTB black hole surrounded by the Quintom field. Indeed, we probe the evolution of the effective potential of such a black hole and possible photon orbits on cosmic epochs. We deduce that passing time in the accelerated universe from the early to late time epochs causes the peak of effective potential to decrease and shift to small radii, while the possibility of forming a stable orbit increases. Besides, four situations including: terminating bound orbit, stable orbit, scattering flyby orbit, and terminating escape orbit have been illustrated in some cosmic time slices. Moreover, changing orbits with time from the early universe to the late time epochs have been investigated. Furthermore, the stability of orbits and ISCO have been analyzed.