Gravitational induction

TL;DR

This paper explores gravitational induction within gravitoelectromagnetism (GEM), demonstrating its analogy to electromagnetic induction laws and discussing its physical implications in the context of general relativity.

Contribution

It introduces the concept of gravitational induction in GEM using a special nonstationary metric, highlighting its analogy to electromagnetic induction laws.

Findings

GEM can model gravitational induction similarly to Faraday's law

A specific nonstationary metric enables explicit gravitational induction

Physical implications of gravitational induction are briefly discussed

Abstract

We study the linear post-Newtonian approximation to general relativity known as gravitoelectromagnetism (GEM); in particular, we examine the similarities and differences between GEM and electrodynamics. Notwithstanding some significant differences between them, we find that a special nonstationary metric in GEM can be employed to show {\it explicitly} that it is possible to introduce gravitational induction within GEM in close analogy with Faraday's law of induction and Lenz's law in electrodynamics. Some of the physical implications of gravitational induction are briefly discussed.