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No Black Hole Theorem in Three-Dimensional Gravity

Daisuke Ida

TL;DR

It is shown in this Letter that a (2+1)-dimensional gravity theory which satisfies the dominant energy condition forbids the existence of a black hole.

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.

No Black Hole Theorem in Three-Dimensional Gravity

TL;DR

It is shown in this Letter that a (2+1)-dimensional gravity theory which satisfies the dominant energy condition forbids the existence of a black hole.

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.

Paper Structure

This paper contains 1 theorem, 9 equations.

Key Result

Theorem 1

Let $(M,g)$ be a three-dimensional space-time subject to the Einstein equation ${\rm Ric}-(R/2)g+\Lambda g=-8\pi T$ with $\Lambda>0$. If the stress-energy tensor $T$ satisfies the dominant energy condition, then $(M,g)$ contains no apparent horizons.

Theorems & Definitions (1)

  • Theorem 1