Distinguishing f(R) theories from general relativity by gravitational lensing effect

• Published in: The European physical journal. C, Particles and fields Vol. 77; no. 11; pp. 1 - 9
• Main Authors: Liu, Hongguang, Wang, Xin, Li, Haida, Ma, Yongge
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-11-2017; Springer; Springer Verlag (Germany); SpringerOpen
• Subjects: Astronomy; Astrophysics; Astrophysics and Cosmology; Elementary Particles; General Relativity and Quantum Cosmology; Hadrons; Heavy Ions; Measurement Science and Instrumentation; Nuclear Energy; Nuclear Physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Regular Article - Theoretical Physics; String Theory; potential: Yukawa; gravitation: lens; gravitation: f(R); general relativity; refractive index; metric: correction; dark matter
• ISSN: 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-017-5308-5

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
f
′
′
(
0
)
/
f
′
(
0
)
is larger than the distance
d
0
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.