Quasi-uniform gravitational field of a disk revisited

TL;DR

This paper revisits the gravitational field of a disk, correcting previous results, analyzing the Riemann tensor, and proving the nonexistence of a truly uniform gravitational field without relying on the weak-field approximation.

Contribution

It provides a revised calculation of the disk's gravitational field, clarifies the nonexistence of uniform gravitational fields, and discusses implications for equations of motion and the Einstein equivalence principle.

Findings

Previous results on disk gravitational fields are shown to be inappropriate.

The Riemann tensor of the disk's gravitational field is explicitly calculated.

The nonexistence of a uniform gravitational field is proven without weak-field assumptions.

Abstract

We calculate the quasi-uniform gravitational field of a disk in the weak-field approximation and demonstrate an inappropriateness of preceding results. The Riemann tensor of this field is determined. The nonexistence of the uniform gravitational field is proven without the use of the weak-field approximation. The previously found difference between equations of motion for the momentum and spin in the accelerated frame and in the quasi-uniform gravitational field also takes place for the disk. However, it does not violate the Einstein equivalence principle because of the nonexistence of the uniform gravitational field.