Hyperbolic motion generated by inversion
Abstract
An inversion transformation applied to an inertial observer is used to generate a nonstatic conformally flat geometry in spherical coordinates. A static observer in the new geometry is uniformly accelerating with respect to the inertial one and vice versa, but its acceleration g undergoes the transformation g → 1/b2g, where b is a constant. A nongeodesic congruence of a static observer has a scalar expansion which grows linearly with time but the acceleration is proportional to r, as for the classical rotation.
0