BTZs

BTZs refers to BTZ black holes, a family of solutions to Einstein gravity in three spacetime dimensions with a negative cosmological constant, named after Baños, Teitelboim and Zanelli. Discovered in 1992, they provide a nontrivial black-hole geometry in a setting with no local gravitational degrees of freedom. The spacetime is asymptotically anti-de Sitter (AdS3) and is fully specified by two global parameters: mass M and angular momentum J. The metric admits an event horizon; for rotation, there are inner horizons, and the radii r_± are determined by M, J and the AdS length l.

In the non-rotating limit (J = 0), the solution reduces to a simple horizon radius r_+ = l sqrt(M). The BTZ black hole is characterized by its outer horizon r_+ and, if present, the inner horizon r_-; its causal structure differs in important ways from higher-dimensional black holes due to the absence of local gravitational degrees of freedom in three dimensions.

Thermodynamics: The BTZ black hole has an entropy S = (2π r_+)/(4 G3) = π r_+/(2 G3) and a temperature T = (r_+^2 - r_-^2)/(2π l^2 r_+). Extensions include charged BTZ solutions and rotating or hairier variants that incorporate additional fields. These models retain many features of higher-dimensional black holes while remaining exactly solvable.

Significance: Because the model is analytically tractable and admits a holographic dual in two dimensions, BTZ black holes provide a useful arena for studying quantum gravity, black-hole thermodynamics, and aspects of the AdS/CFT correspondence. They remain a standard reference point in theoretical investigations of lower-dimensional gravity and holography.