https://doi.org/10.1140/epjc/s10052-017-5308-5
Regular Article - Theoretical Physics
Distinguishing f(R) theories from general relativity by gravitational lensing effect
1
Department of Physics, Beijing Normal University, Beijing, 100875, China
2
Centre de Physique Théorique (UMR 7332), Aix Marseille Université and Université de Toulon, 13288, Marseille, France
* e-mail: mayg@bnu.edu.cn
Received:
30
August
2017
Accepted:
12
October
2017
Published online:
30
October
2017
The post-Newtonian formulation of a general class of f(R) theories is set up in a third-order approximation. It turns out that the information of a specific form of f(R) gravity is encoded in the Yukawa potential, which is contained in the perturbative expansion of the metric components. Although the Yukawa potential is canceled in the second-order expression of the effective refraction index of light, detailed analysis shows that the difference of the lensing effect between the f(R) gravity and general relativity does appear at the third order when 
is larger than the distance 
to the gravitational source. However, the difference between these two kinds of theories will disappear in the axially symmetric spacetime region. Therefore only in very rare case the f(R) theories are distinguishable from general relativity by gravitational lensing effect in a third-order post-Newtonian approximation.
© The Author(s), 2017
