Local spacetime effects on gyroscope systems

TL;DR

This paper provides a detailed theoretical analysis of how spacetime curvature affects gyroscope-based frame synchronization and proposes an experiment to distinguish between Kerr and Schwarzschild metrics.

Contribution

It introduces a precise model for gyroscope transport in curved spacetime and suggests a practical experiment to identify spacetime rotation effects.

Findings

Gyroscope systems lose synchronization due to spacetime curvature and motion.

The proposed experiment can distinguish Kerr from Schwarzschild spacetime.

Initial alignment of gyroscopes is affected by gravitational effects.

Abstract

We give a precise theoretical description of initially aligned sets of orthogonal gyroscopes which are transported along different paths from some initial point to the same final point in spacetime. These gyroscope systems can be used to synchronize separated observers' spatial frames by free fall along timelike geodesics. We find that initially aligned gyroscope systems, or spatial frames, lose their synchronization due to the curvature of spacetime and their relative motion. On the basis of our results we propose a simple experiment which enables observers to determine locally whether their spacetime is described by a rotating Kerr or a non-rotating Schwarzschild metric.