New Geometry with All Killing Vectors Spanning the Poincaré Algebra

The new four-dimensional geometry whose Killing vectors span the Poincaré algebra is presented and its structure is analyzed. The new geometry can be regarded as the Poincaré-invariant solution of the degenerate extension of the vacuum Einstein field equations with a negative cosmological constant and provides a static cosmological spacetime with a Lobachevsky space. The motion of free particles in the spacetime is discussed.