on the equivalence of fields of acceleration and gravitation

The question of whether the same acceleration field that is found in a rigid uniformly rotating disc can annul a gravitational field is answered in the negative because their curvatures are different. There is an exact correspondence between a uniformly rotating disc and hyperbolic geometry of constant curvature, while, gravitational fields require non-constant, negative curvature. The connection between the two is the free-fall time; the former has constant density while the latter, constant mass. The distortion caused by motion is experienced in the hyperbolic world when the rim of the κ-disc is approached, where κ is the disc radius that determines the nature of the fields. Characteristic hyperbolic properties can thus be used to explain relativistic phenomena, like the angle defect in relation to the FitzGerald-Lorentz contraction, the electromagnetic Poincaré stress, aberration which violates of the laws of cosines and sines, gravitational frequency shifts and the bending of light near a massive object.