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.
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The BTZ black hole is a three-dimensional vacuum spacetime with negative cosmological constant . 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]
The Black Hole in Three Dimensional Spacetime by Máximo Bañados and others. Equations (1)–(3) and final geometric discussion
For and , writeThis convention chooses nonnegative angular momentum. Restoring the three-dimensional gravitational constant , its mass and angular momentum areThe outer Killing horizon at has angular velocity and surface gravityThus gives the nonrotating case, while gives a degenerate Killing horizon. The latter has zero limiting Hawking temperature and nonzero horizon circumference.