The BTZ black hole is a quotient of three-dimensional Anti-de Sitter spacetime. In lapse-and-shift coordinates its outer and inner horizon radii are and , and its outer-horizon surface gravity is
Forthe transformations and givewhich is regular at every horizon where vanishes while remains finite.
For the nonrotating BTZ metric in ingoing coordinates, future null normals to a circle of fixed may be chosen as and . Their expansions are and , so both are negative inside the outer horizon.
The BTZ black hole can be null-geodesically incomplete at even though every local curvature invariant is finite there. The endpoint comes from the global anti-de Sitter quotient rather than curvature blowup.
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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.