New Geometry with All Killing Vectors Spanning the Poincar\'e Algebra
Chao-Guang Huang, Yu Tian, Xiao-Ning Wu, Zhan Xu, Bin Zhou
TL;DR
This paper introduces a novel 4D geometry with Killing vectors forming the Poincaré algebra, analyzing its structure and implications as a Poincaré-invariant solution with a Lobachevsky space, relevant for understanding particle motion.
Contribution
It presents a new geometry where all Killing vectors span the Poincaré algebra, extending vacuum Einstein solutions with a negative cosmological constant.
Findings
The geometry is Poincaré-invariant and static.
It features a Lobachevsky space as a cosmological solution.
Particle motion in this space is characterized and discussed.
Abstract
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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