Linearized Analysis of Rastall Gravity

TL;DR

This paper performs a linearized analysis of Rastall gravity, deriving metrics and exploring gravitoelectromagnetic effects, revealing how non-conservation of matter influences gravitational fields and forces.

Contribution

It introduces a linearized formalism for Rastall gravity and analyzes its gravitoelectromagnetic implications, a novel approach in this modified gravity theory.

Findings

Derived the linearized metric for localized matter in Rastall gravity

Analyzed gravitoelectric and gravitomagnetic fields for a moving observer

Showed the gravitomagnetic field is perpendicular to the observer's motion

Abstract

Rastall gravity is a generalization of the Einstein gravity in which the matter is not conserved in the presence of a non-constant spacetime curvature. In this report, we analyze Rastall gravity using the linearized formalism. The linearized metric for a localized matter without pressure and shear stress is obtained, and a spherically symmetric metric for a non-rotating mass is derived. A phenomenological consequence, known as the gravitoelectromagnetism, is subsequently discussed in detail, where it is shown that a free-falling observer will see the motion of a nearby free particle as being subject to a velocity-independent gravitoelectric force and a velocity-dependent gravitomagnetic force. An explicit calculation of the gravitoelectric and gravitomagnetic fields as seen by an observer moving in a circular orbit in a spherically symmetric gravitational field is presented, and it is shown that the resulting gravitomagnetic field is perpendicular to the observer's moving direction.