On reversal of centrifugal acceleration in special relativity

TL;DR

This paper examines the controversial phenomenon of centrifugal acceleration reversal in special relativity, clarifying its frame dependence and contrasting it with general relativistic effects like the black hole horizon and photon orbit.

Contribution

It demonstrates that centrifugal acceleration reversal is frame-dependent and clarifies its relation to relativistic time dilation and coordinate effects, contrasting with true physical reversals in general relativity.

Findings

Centrifugal acceleration reversal is frame-dependent and not observed by proper observers.

The velocity of a relativistic bead approaches the speed of light at the light cylinder.

In general relativity, centrifugal force reverses at the photon orbit r=3M.

Abstract

The basic principles of General Theory of Relativity historically have been tested in gedanken experiments in rotating frame of references. One of the key issues, which still evokes a lot of controversy, is the centrifugal acceleration. Machabeli & Rogava (1994) argued that centrifugal acceleration reverse direction for particles moving radially with relativistic velocities within a "bead on a wire" approximation. We show that this result is frame-dependent and reflects a special relativistic dilution of time (as correctly argued by de Felice (1995)) and is analogous to freezing of motion on the black hole horizon as seen by a remote observer. It is a reversal of coordinate acceleration; there is no such effect as measured by a defined set of observers, e.g., proper and/or comoving. Frame-independent velocity of a "bead" with respect to stationary rotating observers increases and formally reaches the speed of light on the light cylinder. In general relativity, centrifugal force does reverse its direction at photon circular orbit, r=3M in Schwarzschild metric, as argued by Abramowicz (1990).