A note: graviton spin, gravitomagnetic fields and self-interaction of non-inertial frame of reference

TL;DR

This paper explores weak gravitational effects related to gravitomagnetic fields, including the spin of gravitational fields, spin-rotation coupling, and self-interaction in non-inertial rotating frames, revealing new insights into gravitational self-interactions.

Contribution

It introduces a gravitational self-interaction mechanism in non-inertial frames, extending the understanding of gravitomagnetic effects and spin interactions in linearized gravity.

Findings

Derived the expression for gravitational field spin using Noether's theorem.

Identified the gravitomagnetic nature of Mashhoon's spin-rotation coupling.

Showed that rotating frames with fluctuating angular velocity exhibit weak self-interactions.

Abstract

Three weak gravitational effects associated with the gravitomagnetic fields are taken into account in this paper: (i) we discuss the background Lorentz transformation and gauge transformation in a linearized gravity theory, and obtain the expression for the spin of gravitational field by using the canonical procedure and Noether theorem; (ii) we point out that by using the coordinate transformation from the fixed frame to the rotating frame, it is found that the nature of Mashhoon's spin-rotation coupling is in fact an interaction between the gravitomagnetic moment of a spinning particle and the gravitomagnetic fields. The fact that the rotational angular velocity of a rotating frame can be viewed as a gravitomagnetic field is demonstrated; (iii) a purely gravitational generalization of Mashhoon's spin-rotation coupling, i.e., the interaction of the graviton spin with the gravitomagnetic fields is actually a self-interaction of the spacetime (gravitational fields). In the present paper, we will show that this self-interaction will also arise in a non-inertial frame of reference itself: specifically, a rotating frame that experiences a fluctuation of its rotational frequency (i.e., the change in the rotational angular frequency) will undergo a weak self-interaction. The self-interaction of the rotating frame, which can also be called the self-interaction of the spacetime of the rotating frame, is just the non-inertial generalization of the interaction of the graviton spin with the gravitomagnetic fields.