The static spacetime relative acceleration for the general free fall and its possible experimental test

TL;DR

This paper derives a covariant expression for the relative acceleration during free fall in static spacetimes, linking it to Fermi coordinates, and proposes an experiment with relativistic beams to test this theoretical result.

Contribution

It provides a covariant formulation of relative free fall acceleration in static spacetimes and connects it with Fermi coordinate expressions, suggesting an experimental test.

Findings

Derived covariant relative acceleration formula for free fall.

Linked the covariant expression with Fermi coordinate results.

Proposed an experimental test using relativistic beams in accelerators.

Abstract

Mishra has recently established, using a generic static metric, the relative local proper-time 3-acceleration of a test-particle in one-dimensional free fall relative to a static reference frame in any static spacetime. In this paper, on the grounds of gravitoelectromagnetism we establish, in a covariant spacetime form, the relative 4-acceleration for the general free fall, indicating its canonical representation with its 3-space cinematical content. Then we obtain the relation between this representation and the very known expression for the relative free fall acceleration in Fermi coordinates. Taking this into account, it is shown that an experiment with relativistic beams in a circular accelerator, modelled by Fermi coordinates, recently proposed by Moliner et al, can test the here established covariant result and, therefore, can also verify Mishra's formula. This possibility of experimental verification, besides its intrinsic importance, can answer a recent inquire by Vigier, related to his recent proposal of derivation of inertial forces.