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

Abstract

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

25 pages, 3 figures; some misprints corrected

References in corpus (6)

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• On Special Relativity with Cosmological Constant
• On Beltrami Model of de Sitter Spacetime
• Mechanics and Newton-Cartan-Like Gravity on the Newton-Hooke Space-time
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• On Principle of Inertia in Closed Universe
• The Principle of Relativity, Kinematics and Algebraic Relations
• The Principle of Relativity and Special Relativity Triple
• Acceleration-extended Newton-Hooke symmetry and its dynamical realization
• Geometries for Possible Kinematics
• On Torsion-free Vacuum Solutions of the Model of de Sitter Gauge Theory of Gravity (II)
• From the Complete Yang Model to Snyder's Model, de Sitter Special Relativity and Their Duality
• Some Peculiarities of Newton-Hooke Space-Times