A static, asymptotically flat, spherically symmetric solutions is
investigated in f(R) theories of gravity for a charged black hole. We have
studied the weak field limit of f(R) gravity for the some f(R) model such as
f(R) = R + epsilon h(R). In particular, weconsider the case lim_{R =0} {h(R)/
dh(R)/dR}=0 and find the space time metric for f(R) = R + {mu}^{4} /R and f(R)
= R^{1-epsilon} theories of gravity far away a charged mass point
In this paper, using f (R) theory of gravity we explicitly calculate cosmological evolution in the presence of a perfect fluid source in four-and fivedimensional, spacetime in which this cosmological evolution in self-creation is presented by Reddy et al 2009 Int. J. Theor. Phys. 48 10. An exact cosmological model is presented using a relation between Einsteins gravity field equation components due to a metric with the same component from f (R) theory of gravity. Some physics and kinematical properties of the model are also discussed.
The spherically symmetric solution for the weak field limit of f (R) gravity in the large scale is investigated. It is shown that, in the weak field limit, the standard Newtonian potential is corrected by a small term which reduces to zero when coupling constant tends to zero. For the considered models, we determine the space-time metric which reduce to general relativity in the zero order limit.
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