In this paper, we first extract general uncharged accelerating BTZ black hole
solutions and study some of their properties. Our analysis shows that
spacetime’s asymptotical behavior depends on four parameters: the cosmological
constant, mass, acceleration, and topological constant. Then, we study the
temperature of these black holes and find a divergence point, which this point
reveals a phase transition between physical and non-physical black holes. Next,
we extend our study for extracting charged accelerating BTZ black hole
solutions in the presence of a nonlinear electrodynamics field known as
conformally invariant Maxwell. Our findings indicate a coupling between the
electrical charge and other quantities of the accelerating BTZ black holes. The
asymptotical behavior of charged accelerating BTZ black holes depends on six
parameters: the cosmological constant, the electrical charge, mass, the
acceleration parameter, the topological constant, and the angular coordinate.
Finally, we investigate the effects of various parameters on the temperature of
these black holes. There are two exciting behaviors for the temperature by
considering different cosmological constant values. When the cosmological
constant is negative, a divergence point and a root exist for the temperature.
The temperature is positive between the divergence point and the root. However,
for the positive value of the cosmological constant, there are four critical
points in the temperature; three roots and a divergence point. These points
provide information about phase transitions between physical and non-physical
black holes.

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