A note on the gravitoelectromagnetic analogy

TL;DR

This paper explores the gravitoelectromagnetic analogy in weak-field Einstein equations, analyzing how gravitational effects can be described using Maxwell-like equations and their application to test particle motion.

Contribution

It clarifies the definition of gravitoelectromagnetic fields in non-stationary conditions and assesses their effectiveness in describing test particle dynamics.

Findings

Gravitoelectromagnetic fields can be defined in non-stationary regimes.

The Maxwell-like equations provide a useful analogy for gravitational effects.

Lorentz-like force equations can describe test particle motion in this framework.

Abstract

We discuss the linear gravitoelectromagnetic approach used to solve Einstein equations in the weak-field and slow-motion approximation, which is a powerful tool to explain, by analogy with electromagnetism, several gravitational effects in the Solar System, where the approximation holds true. In particular, we discuss the analogy according to which Einstein equations can be written as Maxwell-like equations and focus on the definition of the gravitoelectromagnetic fields in non stationary conditions. Furthermore, we examine to what extent, starting from a given solution of Einstein equations, gravitoelectromagnetic fields can be used to describe the motion of test particles using a Lorentz-like force equation