n-dimensional anti-de Sitter space (AdSn) is a maximally symmetric Lorentzian manifold with constant negative scalar curvature.

Manifolds of constant curvature are most familiar in the case of two dimensions, where the surface of a sphere is a surface of constant positive curvature, a flat (Euclidean) plane is a surface of constant zero curvature, and a hyperbolic plane is a surface of constant negative curvature.

Einstein's general theory of relativity places space and time on equal footing, so that one considers the geometry of a unified spacetime instead of considering space and time separately. The cases of spacetime of constant curvature are de Sitter space (positive), Minkowski space (zero), and anti-de Sitter space (negative). As such, they are exact solutions of Einstein's field equations for an empty universe with a positive, zero, or negative cosmological constant, respectively.

I solved the Einstein field equation for hyperboilic spacetime with metric signature (+,-,-). i found that hyperbolic geometry has comnstant negative curvature which resembles with definition of anti-de sitter spacetime means this is an considerable exact solution of einstein field equation