Gravitoelectromagnetism in metric f(R) and Brans–Dicke theories with a potential

Abstract

A Gravitoelectromagnetism formalism in the context of metric f (R) theory is presented and the analogue Lorentz force law is derived. Some interesting results such as the dependence of the deviation from General Relativity on the absolute value of the scalar potential are found, it is also found that the f (R) effects are only relevant at a shorter distance or when the distance is much less than the compton wavelength, and that the effects are attractive in nature. An investigation of gravitational time delay in the context of metric f (R) is also presented showing that the Ricci scalar alone is responsible for the time delay effect which seems to suggest that the extra scalar degree of freedom associated to f (R) does not provide any modification. Also, to generalise our results, the Lorentz force law and gravitational time delay in the case of Brans-Dicke theories with a potential are derived; it is shown that the results are consistent with those obtained in the case of metric f (R) and General Relativity in the appropriate limits.

Multipole analysis for linearizedf(R)gravity with irreducible Cartesian tensors

“…It is easy to verify that for the source rotating around the z-axis, the above metric can recover that for a point-like source in Refs. [6,19,20]. Further, if the leading pole moments are considered in the static spacetime, the above metric can also recover that for a ball-like source in Ref.…”

“…The first two effects are those of GR-like precession at the leading pole order, and they can indeed recover classical geodesic effect and Lense-Thirring effect in GR, respectively. The f (R)-monopole effect provides the most main correction in f (R) gravity, and it can reduce to that for the gyroscope moving around a point-like [6,20] or a ball-like source [21]. The Thomas-monopole effect gives the most main correction to the result in Special Relativity.…”

“…In Ref. [20], the influence of the Earth's oblateness on gyroscopic precession is considered, but the effective constraint on a is not obtained. Based on the effects of the β up to 1/c 3 order, those of both transformations, A ρ…”

“…When the leading pole moments are considered in the stationary spacetime, the GR-like part can recover the Lense-Thirring metric, and the f (R) part provides the Yukawa-like correction in f (R) gravity, so the metric can easily reduce to that for a point-like source in Refs. [6,19,20].…”

Gravitoelectromagnetism, Solar System Tests, and Weak-Field Solutions in f (T,B) Gravity with Observational Constraints

“…Similar to Ref. [92], one obtains the first two terms which are found in GR (except for a gravitational constant rescaling from f T (0, 0)) with a new contribution arising from the scalar mode. However, if the scalar mode is absent (i.e.…”