Hyperbolic nature of uniformly rotating systems and their relation to gravity

Details Hyperbolic nature of uniformly rotating systems and their relation to gravity Hyperbolic nature of uniformly rotating systems and their relation to gravity

2008-04-10

arxiv.org/abs/0804.1674v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

8 pages, 1 figure

Scientific paper

Special relativity corresponds to hyperbolic geometry at constant velocity while the so-called general relativity corresponds to hyperbolic geometry of uniformly accelerated systems. Generalized expressions for angular momentum, centrifugal and Coriolis forces are found in hyperbolic space, which reduce to the usual expressions of Euclidean space when the absolute constant tends to infinity. Gravity enters only in the specification of the absolute constant. A uniformly rotating disc corresponds exactly to hyperbolic geometry with a constant negative Gaussian curvature. The angle defect is related to Lorentz contraction of objects normal to the radial direction. Lobachevsky's angle of parallelism accounts for the apparent relativistic distortion of moving objects and would provide a testing ground to measure a positive defect by replacing large distances by high speeds that are comparable with that of light.

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