The Problem of Inertia in Friedmann Universes

TL;DR

This paper investigates the origin of inertia in Friedmann universes using Sciama's law, linking electromagnetic analogies to gravitational inertia and deriving how cosmic parameters influence inertial forces.

Contribution

It provides covariant electromagnetic field expressions in Friedmann models and applies Sciama's law to relate matter distribution to inertia, considering cosmological parameters.

Findings

Inertial force is proportional to acceleration with a factor depending on cosmological parameters.

The inertial coefficient k varies with matter density, dark energy, and redshift.

The approach links electromagnetic analogies to gravitational inertia in curved spacetime.

Abstract

In this paper we study the origin of inertia in a curved spacetime, particularly the spatially flat, open and closed Friedmann universes. This is done using Sciama's law of inertial induction, which is based on Mach's principle, and expresses the analogy between the retarded far fields of electrodynamics and those of gravitation. After obtaining covariant expressions for electromagnetic fields due to an accelerating point charge in Friedmann models, we adopt Sciama's law to obtain the inertial force on an accelerating mass $m$ by integrating over the contributions from all the matter in the universe. The resulting inertial force has the form $F = -kma$, where $k < 1 $ depends on the choice of the cosmological parameters such as $\Omega_{M}$, $\Omega_{\Lambda}$, and $\Omega_{R}$ and is also red-shift dependent.