Inertial frame dragging and Mach's principle in General Relativity

TL;DR

This paper introduces a new parameter called the 'cumulative drag index' to analyze inertial frame dragging in Kerr and G"odel spacetimes, exploring its implications for Mach's principle in general relativity.

Contribution

It defines and studies a novel parameter to quantify inertial frame dragging, linking local physics to the influence of the universe, thus providing a new perspective on Mach's principle.

Findings

The cumulative drag index behaves similarly for co and counter rotating particles.

The index suggests a potential Machian influence of the universe on local inertial frames.

The study connects frame dragging effects in specific solutions to broader philosophical questions.

Abstract

We define a new parameter `cumulative drag index' for a particle in circular orbit in a stationary, axisymmetric gravitational field and study its behaviour in the two well known solutions of general relativity {\it viz.}, the Kerr spacetime and the G\"odel spacetime, wherein the inertial frame dragging has an important role. As it shows similar behaviour for both co and counter rotating particles, it may indeed be an indication of the influence of the faraway universe on local physics and thus Machian.