In this paper, general uncharged accelerating BTZ black hole solutions are extracted and studied some of their properties. The analysis shows that spacetime’s asymptotic behavior depends on four parameters: the cosmological constant, mass, acceleration, and topological constant. Then, the temperature of these black holes are studied and it is found that the temperature is always positive for AdS spacetime. Next, the study is extended for extracting charged accelerating BTZ black hole solutions in the presence of a nonlinear electrodynamics field known as conformally invariant Maxwell. The findings indicate a coupling between the electrical charge and other quantities of the accelerating BTZ black holes. The asymptotic behavior of charged accelerating BTZ black holes depends on five parameters: the cosmological constant, the electrical charge, mass, the acceleration parameter, and the topological constant. Then, the effects of charge, acceleration parameters, and the topological constant on the root of these black holes are studied. Finally, the temperature of these black holes in AdS spacetime is investigated. For these black holes, the temperature depends on the electrical charge, accelerating parameter, and the cosmological constant. The analysis indicates that the temperature of charged accelerating BTZ AdS black holes is always positive.
