Apparent superluminal velocities due to the curvature of space

Abstract

Instead of the difficult concept of a three-dimensional curved space one can use two partial models of two-dimensional curved subspaces. If a two-dimensional subspace is curved the arbitrary angle of view must have a distorted shape which has in consequence an optical illusion. The distorted shape of ϕ must be corrected to the real angle1φ, valid in uncurved space according to the relation φ=1φf(ρ) where ρ is the central angle in theoretical sphere. If a two-dimensional subspace is just a spheric surface, the correction factor isfs(ρ)≅ρ/sin ρ, appropriate to the angle distance ρ from observer to the observed object.