Notes on no black hole theorem in three dimensional gravity

In this paper, we revisit the no black hole theorem in three dimensional (3D) gravity in the Newman-Penrose formalism in a generalized Newman-Unti gauge. After adapting the well established 4D NP formalism and its gauge and coordinates system to 3D gravity, we show that the no black hole theorem is manifest in the NP equations. We further study in detail the horizon properties of the 3D charged rotating solutions and confirm that a black hole solution requires a negative cosmological constant.