The Black Hole in Three Dimensional Space Time

TL;DR

This paper explores black hole solutions in 2+1 dimensional spacetime with a negative cosmological constant, revealing similarities to 3+1 black holes and analyzing their thermodynamic properties.

Contribution

It demonstrates the existence of black hole solutions in 2+1 dimensions with charge and angular momentum, and evaluates their entropy and spectrum.

Findings

Black holes in 2+1 dimensions exist with mass, charge, and angular momentum.

The entropy equals twice the horizon perimeter.

Anti-de Sitter space forms a negative energy state with a mass gap.

Abstract

The standard Einstein-Maxwell equations in 2+1 spacetime dimensions, with a negative cosmological constant, admit a black hole solution. The 2+1 black hole -characterized by mass, angular momentum and charge, defined by flux integrals at infinity- is quite similar to its 3+1 counterpart. Anti-de Sitter space appears as a negative energy state separated by a mass gap from the continuous black hole spectrum. Evaluation of the partition function yields that the entropy is equal to twice the perimeter length of the horizon.