Rotation of inertial frames by angular momentum of matter and waves

TL;DR

This paper investigates how rotating matter and gravitational waves can drag inertial frames, demonstrating that Machian effects are present in both material shells and gravitational wave pulses, using a simplified approach.

Contribution

It introduces a new, simpler method to analyze the dynamics of rotating shells and shows their frame dragging effects align with those of gravitational wave pulses, highlighting Machian principles.

Findings

Rotating shells can drag inertial frames within them.

Gravitational wave pulses exhibit similar frame dragging effects.

Machian effects are consistent across material and gravitational sources.

Abstract

We elucidate the dynamics of a thin spherical material shell with a tangential pressure, using a new approach. This is both simpler than the traditional method of extrinsic curvature junction conditions (which we also employ), and suggests an expression for a `gravitational potential energy' of the shell. Such a shell, if slowly spinning, can rotationally drag the inertial frames within it through a finite angle as it collapses and rebounds from a minimum radius. Rebounding `spherical' and cylindrical pulses of rotating gravitational waves were studied previously. Here we calculate their angular momentum and show that their rotational frame dragging is in agreement with that of the rotating spherical shell and a rotating cylindrical dust shell. This shows that Machian effects occur equally for material and analogous `immaterial' sources.