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arXiv · 2104.07529

Multipole analysis on gyroscopic precession in $f(R)$ gravity with irreducible Cartesian tensors

Bofeng Wu·Xin Zhang
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Abstract

In $f(R)$ gravity, the metric, presented in the form of the multipole expansion, for the external gravitational field of a spatially compact supported source up to $1/c^3$ order is provided, where $c$ is the velocity of light in vacuum. The metric consists of General Relativity-like part and $f(R)$ part, where the latter is the correction to the former in $f(R)$ gravity. At the leading pole order, the metric can reduce to that for a point-like or ball-like source. For the gyroscope moving around the source without experiencing any torque, the multipole expansions of its spin's angular velocities of gravitoelectric-type precession, gravitomagnetic-type precession, $f(R)$ precession, and Thomas precession are all derived. The first two types of precession are collectively called General Relativity-like precession, and the $f(R)$ precession is the correction in $f(R)$ gravity. At the leading pole order, these expansions can recover the results for the gyroscope moving around a point-like or ball-like source. If the gyroscope has a nonzero four-acceleration, its spin's total angular velocity of precession up to $1/c^3$ order in $f(R)$ gravity is the same as that in General Relativity.

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BibTeXRIS

Bofeng Wu, Xin Zhang. 2021-04-15. Multipole analysis on gyroscopic precession in $f(R)$ gravity with irreducible Cartesian tensors. https://doi.org/10.1103/physrevd.104.024052

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