 BTZ black hole

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.

A BTZ black hole, named after physicists Stefan Banados, Claudio Teitelboim, and Jorge Zanelli, is a solution to Einstein's equations of general relativity in a lower-dimensional (specifically 2+1 dimensions) spacetime with a negative cosmological constant. The BTZ black hole provides a model for a black hole that captures many of the properties of higher-dimensional black holes but is simpler due to its lower dimensionality.