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arXiv · 2505.05499

Linearized Analysis of Rastall Gravity

Yuwadee Tongkong
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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.

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Yuwadee Tongkong. 2025-05-06. Linearized Analysis of Rastall Gravity. https://arxiv.org/abs/2505.05499

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