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ISSN: 1434-6044, SCI

Perturbative solutions of the f (R)-theory of gravity in a central gravitational field and some applications

Nguyen Anh Ky, Pham Van Ky, Nguyen Thi Hong Van

Exact solutions of an f (R)-theory (of gravity)in a static central (gravitational) field have been studied in the literature quite well, but, to find and study exact solutions in the case of a non-static central field are not easy at all. There are, however, approximation methods of finding a solution in a central field which is not necessarily static. It is shown in this article that an approximate solution of an f (R)- theory in a general central field, which is not necessary to be static, can be found perturbatively around a solution of the Einstein equation in the general theory of relativity. In particular, vacuum solutions are found for f (R) of general and some special forms. Further, applications to the investigation of a planetary motion and light’s propagation in a central field are presented. An effect of an f (R)-gravity is also estimated for the SgrA*–S2 system. The latter gravitational system is much stronger than the Sun–Mercury system, thus the effect could be much stronger and, thus, much more measurable.

URL: https://doi.org/10.1140/epjc/s10052-018-6023-6