Newton-Hooke Limit of Beltrami-de Sitter Spacetime, Principles of Galilei-Hooke's Relativity and Postulate on Newton-Hooke Universal Time

摘要

Based on the Beltrami-de Sitter spacetime, we present the Newton-Hooke modelunder the Newton-Hooke contraction of the $BdS$ spacetime with respect to thetransformation group, algebra and geometry. It is shown that in Newton-Hookespace-time, there are inertial-type coordinate systems and inertial-typeobservers, which move along straight lines with uniform velocity. And they areinvariant under the Newton-Hooke group. In order to determine uniquely theNewton-Hooke limit, we propose the Galilei-Hooke's relativity principle as wellas the postulate on Newton-Hooke universal time. All results are readilyextended to the Newton-Hooke model as a contraction of Beltrami-anti-de Sitterspacetime with negative cosmological constant.