Thomas Precession by Uniform Acceleration and Gravity

Abstract

We determine nonlinear transformations between coordinate systems which are mutually in a constant symmetrical accelerated motion. The maximal acceleration limit follows from the kinematical origin and it is an analogue of the maximal velocity in special relativity. We derive the dependence of mass, length, time, Doppler effect, Čerenkov effect and transition radiation angle on acceleration as an analogue phenomenon in special theory of relativity. The last application of our method is the Thomas precession by uniform acceleration and equivalent gravity with the possible role in modern physics and cosmology.

The Black Hole Binary Gravitons and Related Problems

“…There is the fundamental problem concerning the maximal mass of the black hole. The theory of the space-time with maximal acceleration constant was derived by authors [56,57]. In this theory the maximal acceleration constant is the analogue of the maximal velocity in special theory of relativity.…”