The Coriolis field

TL;DR

This paper explores the Coriolis field within Newton-Cartan theory, illustrating its properties, solutions, and detection methods, and extends the discussion to its manifestation in general relativity with experimental considerations.

Contribution

It provides a comprehensive pedagogical analysis of the Coriolis field, linking Newtonian and relativistic frameworks, and discusses experimental detection techniques.

Findings

Coriolis field satisfies Newton-Cartan equations.

Solutions include a Newtonian analogue of the G"odel universe.

Detection methods involve gyroscope-based experiments like Gravity Probe B.

Abstract

We present a pedagogical discussion of the Coriolis field, emphasizing its not-so-well-understood aspects. We show that this field satisfies the field equations of the so-called Newton-Cartan theory, a generalization of Newtonian gravity that is covariant under changes of arbitrarily rotating and accelerated frames. Examples of solutions of this theory are given, including the Newtonian analogue of the G\"odel universe. We discuss how to detect the Coriolis field by its effect on gyroscopes, of which the gyrocompass is an example. Finally, using a similar framework, we discuss the Coriolis field generated by mass currents in general relativity, and its measurement by the Gravity Probe B and LAGEOS/LARES experiments.