BTZ black hole

Lore & Background

The BTZ black hole was discovered in 1992 by Bañados, Teitelboim, and Zanelli. This came as a surprise because when the cosmological constant is zero, a vacuum solution of (2+1)-dimensional gravity is necessarily flat, and no black hole solutions with event horizons exist. However, thanks to the negative cosmological constant, the BTZ black hole has remarkably similar properties to the 3+1 dimensional Schwarzschild and Kerr black hole solutions, which model real-world black holes.

The BTZ black hole admits a no hair theorem, fully characterizing the solution by its ADM-mass, angular momentum, and charge. It has the same thermodynamical properties as traditional black hole solutions, such as Schwarzschild or Kerr black holes, with its entropy captured by a law directly analogous to the Bekenstein bound in (3+1)-dimensions, essentially with the surface area replaced by the BTZ black hole's circumference. Like the Kerr black hole, a rotating BTZ black hole contains an inner and an outer horizon, analogous to an ergosphere.

Reader's Guide

The BTZ black hole is significant because it provides a tractable model of a black hole in lower-dimensional gravity, allowing for detailed study of black hole thermodynamics and quantum gravity. 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, but it was shown that this black hole could arise from collapsing matter. The BTZ solution is often discussed in the realm of (2+1)-dimensional quantum gravity. Its metric in the absence of charge is given by a specific formula involving the black hole radii and the radius of AdS3 space. BTZ black holes without any electric charge are locally isometric to anti-de Sitter space, corresponding to an orbifold of the universal covering space of AdS3. A rotating BTZ black hole admits closed timelike curves.