All Static Black Holes in AdS$_3$

TL;DR

This paper derives the general static vacuum solutions in three-dimensional gravity with negative cosmological constant, revealing new black hole solutions on AdS3 boundary, including black funnels and droplets, with implications for dual boundary theories.

Contribution

It presents the first comprehensive classification of static vacuum solutions in AdS3, including globally distinct black hole configurations with boundary interpretations.

Findings

New static black hole solutions on AdS3 boundary.

Existence of black funnels and droplets in these solutions.

Duality with Hartle-Hawking state in boundary theory.

Abstract

In this work we find the general static vacuum solution of three dimensional gravity with negative cosmological constant. Even though all solutions are locally diffeomorphic to pure $AdS_{3}$, solutions that differ globally from the latter space exist. New solutions with black holes on the $AdS_3$ boundary are found in both global and Poincare coordinates. In the Poincare coordinates such solutions are known as black funnels and black droplets. The black funnel provided by our general static metric is dual to the Hartle-Hawking state in the $1+1$ boundary theory.