The BTZ black hole, named after Máximo Bañados, Claudio Teitelboim, and Jorge Zanelli, is a black hole solution for (2+1)-dimensional topological gravity with a negative cosmological constant.

History

In 1992, Bañados, Teitelboim, and Zanelli discovered the BTZ black hole solution. This came as a surprise, because when the cosmological constant is zero, a vacuum solution of (2+1)-dimensional gravity is necessarily flat (the Weyl tensor vanishes in three dimensions, while the Ricci tensor vanishes due to the Einstein field equations, so the full Riemann tensor vanishes), and it can be shown that no black hole solutions with event horizons exist. But thanks to the negative cosmological constant in the BTZ black hole, it is able to have remarkably similar properties to the 3+1 dimensional Schwarzschild and Kerr black hole solutions, which model real-world black holes.

Properties

The similarities to the ordinary black holes in 3+1 dimensions: Since (2+1)-dimensional gravity has no Newtonian limit, one might fear that the BTZ black hole is not the final state of a gravitational collapse. It was however shown, that this black hole could arise from collapsing matter and we can calculate the energy-moment tensor of BTZ as same as (3+1) black holes. The BTZ solution is often discussed in the realm on (2+1)-dimensional quantum gravity.

The case without charge

The metric in the absence of charge is where r_+,~r_- are the black hole radii and l is the radius of AdS3 space. The mass and angular momentum of the black hole is BTZ black holes without any electric charge are locally isometric to anti-de Sitter space. More precisely, it corresponds to an orbifold of the universal covering space of AdS3. A rotating BTZ black hole admits closed timelike curves.