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

Abstract

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.

References in corpus (20)

• f(R) Theories Of Gravity
• f(R) theories
• Extended Theories of Gravity
• Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration
• Monitoring stellar orbits around the Massive Black Hole in the Galactic Center
• Are f(R) dark energy models cosmologically viable ?
• Spherically symmetric solutions of modified field equations in f(R) theories of gravity
• Solar System tests DO rule out 1/R gravity
• Spin transfer in an antiferromagnet
• Static Spherically Symmetric Solutions in F(R) Gravity
• Spherically symmetric spacetimes in f(R) gravity theories
• A general solution in the Newtonian limit of f(R)- gravity
• Dust Static Spherically Symmetric Solution in $f(R)$ Gravity
• Generation of spherically symmetric metrics in $f\left(R\right)$ gravity
• Some static spherically symmetric interior solutions of $f(R)$ gravity
• The Post-Newtonian Limit of f(R)-gravity in the Harmonic Gauge
• Future dynamics in f(R) theories
• Spherically Symmetric Solutions in F(R) Gravity and Gravitational Repulsion
• Exact Cosmological Solutions of $f(R)$ Theories via Hojman Symmetry
• Distinguishing f(R) theories from general relativity by gravitational lensing effect

Cited by in corpus (5)

• Non-Singular Black Holes and mass inflation in modified gravity
• Perturbative approach to $f(R)$-gravitation in FLRW cosmology
• Gravitational radiation of a spherically symmetric source in $f(R)$-gravitation
• Nonstatic Reissner-Nordström metric in the perturbative $f(R)$ theory: Embedding in the background of the FLRW cosmology, uniqueness of solutions, the TOV equation
• Metric Variation of the Energy-Momentum Tensor of a Perfect Fluid and Its Applications to Cosmology and Neutron Stars