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The BTZ black hole is a three-dimensional vacuum spacetime with negative cosmological constant $\Lambda =-1/L^2$. Locally it has the constant negative sectional curvature of Anti-de Sitter spacetime, but discrete identifications give it a black-hole causal structure. It is a useful example of horizon geometry and thermodynamics without the local gravitational-wave degrees of freedom of four-dimensional general relativity.^[ref]

For $r_{+}>0$ and $0\le r_{-}\le r_{+}$, writeThis convention chooses nonnegative angular momentum. Restoring the three-dimensional gravitational constant $G_3$, its mass and angular momentum areThe outer Killing horizon at $r_{+}$ has angular velocity $r_{-}/(L{r}_{+})$ and surface gravityThus $r_{-}=0$ gives the nonrotating case, while $r_{-}=r_{+}>0$ gives a degenerate Killing horizon. The latter has zero limiting Hawking temperature and nonzero horizon circumference.

Claudio Teitelboim, with Máximo Bañados and Jorge Zanelli, derived the BTZ black hole and investigated its thermodynamics. Their calculation related temperature and entropy to a three-dimensional black hole's horizon, with entropy proportional to horizon circumference.^[ref]

In three spacetime dimensions the horizon cross-section is a curve, so its length replaces the familiar two-dimensional horizon area.

Jorge Zanelli co-discovered a black-hole solution in three-dimensional spacetime with Máximo Bañados and Claudio Teitelboim. The BTZ black hole exists with a negative cosmological constant and has global horizon and thermodynamic properties despite the simpler local geometry of three-dimensional gravity.^[ref]

The example separates global spacetime structure from the local curvature description.

Máximo Bañados co-developed the BTZ black hole with Claudio Teitelboim and Jorge Zanelli in 1992. It showed that three-dimensional gravity with a negative cosmological constant admits black-hole states characterized by conserved quantities and horizons.^[ref]

This supplied a simpler setting for investigating global gravitational and thermodynamic questions without assuming that all black-hole phenomena require four-dimensional spacetime.