Multipole analysis in the radiation field for linearized $f(R)$ gravity with irreducible Cartesian tensors

Abstract

The $1/r$-expansion in the distance to the source is applied to the linearized $f(R)$ gravity, and its multipole expansion in the radiation field with irreducible Cartesian tensors is presented. Then, the energy, momentum, and angular momentum in the gravitational waves are provided for linearized $f(R)$ gravity. All of these results have two parts which are associated with the tensor part and the scalar part in the multipole expansion of linearized $f(R)$ gravity, respectively. The former is the same as that in General Relativity, and the latter, as the correction to the result in General Relativity, is caused by the massive scalar degree of freedom, and places an important role in distinguishing GR and $f(R)$ gravity.

arXiv comment20 pages. Two important references are added in this new version

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Cited by in corpus (4)

• Multipole analysis for linearized $f(R,\mathcal{G})$ gravity with irreducible Cartesian tensors
• Multipole analysis for linearized $f(R)$ gravity with irreducible Cartesian tensors
• The gravitational field outside a spatially compact stationary source in a generic fourth-order theory of gravity
• Multipole analysis on stationary massive vector and symmetric tensor fields