Notes on no black hole theorem in three dimensional gravity

TL;DR

This paper revisits the no black hole theorem in three-dimensional gravity using the Newman-Penrose formalism, demonstrating its validity and exploring horizon properties of solutions, emphasizing the necessity of a negative cosmological constant for black holes.

Contribution

It adapts the Newman-Penrose formalism to 3D gravity and shows the no black hole theorem is evident within this framework, clarifying conditions for black hole solutions.

Findings

The no black hole theorem is manifest in 3D NP equations.

A black hole solution requires a negative cosmological constant.

Horizon properties of 3D charged rotating solutions are analyzed.

Abstract

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.