Extra force in $f(R)$ modified theories of gravity

Bertolami, Orfeu; Boehmer, Christian G.; Harko, Tiberiu; Lobo, Francisco S. N.

Extra force in $f(R)$ modified theories of gravity

Authors

Bertolami, Orfeu

Boehmer, Christian G.

Harko, Tiberiu

Lobo, Francisco S. N.

Description

The equation of motion for test particles in $f(R)$ modified theories of gravity is derived. By considering an explicit coupling between an arbitrary function of the scalar curvature, $R$, and the Lagrangian density of matter, it is shown that an extra force arises. This extra force is orthogonal to the four-velocity and the corresponding acceleration law is obtained in the weak field limit. Connections with MOND and with the Pioneer anomaly are further discussed.
Revtex4 file, 5 pages. Version to appear in Physical Review D