Gravitational lensing and <Emphasis Type="Italic">f</Emphasis> (<Emphasis Type="Italic">R</Emphasis>) theories in the Palatini approach

We investigate gravitational lensing in the Palatini approach to the f (R) extended theories of gravity. Starting from an exact solution of the f (R) field equations, which corresponds to the Schwarzschild–de Sitter metric and, on the basis of recent studies on this metric, we focus on some lensing observables, in order to evaluate the effects of the nonlinearity of the gravity Lagrangian. We give estimates for some astrophysical events, and show that these effects are tiny for galactic lenses, but become interesting for extragalactic ones.