No Black Hole Theorem in Three-Dimensional Gravity

TL;DR

This paper demonstrates that in (2+1)-dimensional gravity theories satisfying the dominant energy condition, black holes cannot exist, challenging the common understanding that negative cosmological constants are necessary for black hole solutions.

Contribution

It proves a no black hole theorem in three-dimensional gravity under the dominant energy condition, removing the need for a negative cosmological constant.

Findings

Black holes are forbidden in (2+1)-dimensional gravity with dominant energy condition.

Negative cosmological constant is not a necessary condition for black holes in 3D gravity.

Theoretical constraints prevent black hole solutions in this setting.

Abstract

A common property of known black hole solutions in (2+1)-dimensional gravity is that they require a negative cosmological constant. In this letter, it is shown that a (2+1)-dimensional gravity theory which satisfies the dominant energy condition forbids the existence of a black hole to explain the above situation.