Charged dilaton solutions and black hole formation in three dimensions

In this paper, we present the charged dilaton solutions and black hole formation in three dimensions. Firstly we revisit the famous Chan–Mann charged dilaton black hole, describing one parameter family of static charged black hole solution in three dimensional Einstein–Maxwell–Dilaton gravity. This solution with a special parameter choice $$b=4a$$ can lead to the three dimensional string solution. Then we give another class of charged dilaton black hole solution with $$b\ne 4a$$. We discuss their geometrical properties, the horizon structure and the causal structure. The time-dependent solution is also presented, which can characterize the three dimensional charged black hole formation in Einstein–Dilaton gravity. Especially, there is no exact time-dependent solution describing the gravitational collapse to the Chan–Mann charged dilaton black hole. Finally, we discuss the gravitational collapse of a dilaton field in the context of the Cosmic Censorship Conjecture