New Geometry with All Killing Vectors Spanning the Poincar\'e Algebra
classification
🌀 gr-qc
keywords
geometrypoincaralgebracosmologicalkillingspace-timevectorsanalyzed
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The new 4D geometry whose Killing vectors span the Poincar\'e algebra is presented and its structure is analyzed. The new geometry can be regarded as the Poincar\'e-invariant solution of the degenerate extension of the vacuum Einstein field equations with a negative cosmological constant and provides a static cosmological space-time with a Lobachevsky space. The motion of free particles in the space-time is discussed.
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