Abstract
Abstract
A viable weak-field and slow-motion approximation method is constructed in
F(R, RμνRμν, Rμν ρσRμν ρσ
) gravity, a general class of
fourth-order theories of gravity. By applying this method, the metric, presented in the form of
the multipole expansion, outside a spatially compact source up to 1/c
3 order is provided, and
the closed-form expressions for the source multipole moments are all presented explicitly. The
metric consists of the massless tensor part, the massive scalar part, and the massive tensor part,
where the former is exactly the metric in General Relativity, and the latter two are the
corrections to it. It is shown that the corrections bear the Yukawa-like dependence on the two
massive parameters and predict the appearance of six additional sets of source multipole moments,
which indicates that up to 1/c
3 order, there exist six degrees of freedom beyond General
Relativity within F(R, RμνRμν, Rμν ρσRμν ρσ
)
gravity. By means of the metric, for a gyroscope moving around the source without experiencing any
torque, the multipole expansions of its spin's angular velocities of the Thomas precession, the
geodetic precession, and the Lense-Thirring precession are derived, and from them, the corrections
to the angular velocities of the three types of precession in General Relativity can be read
off. These results indicate that differently from f(R) or f(R,𝒢) gravity, the most
salient feature of the general F(R, RμνRμν, Rμν ρσRμν ρσ
)
gravity is that it gives the nonvanishing correction to
the gyroscopic spin's angular velocity of the Lense-Thirring precession in General Relativity.