  A number of recent observations have suggested that the Einstein's theory of
general relativity may not be the ultimate theory of gravity. The f(R) gravity
model with R being the scalar curvature turns out to be one of the best bet to
surpass the general relativity which explains a number of phenomena where
Einstein's theory of gravity fails. In the f(R) gravity, behaviour of the
spacetime is modified as compared to that of given by the Einstein's theory of
general relativity. This theory has already been explored for understanding
various compact objects such as neutron stars, white dwarfs etc. and also
describing evolution of the universe. Although, researchers have already found
the vacuum spacetime solutions for the f(R) gravity, yet there is a caveat that
the metric does have some diverging terms and hence these solutions are not
asymptotically flat. We show that it is possible to have asymptotically flat
spherically symmetric vacuum solution for the f(R) gravity, which is different
from the Schwarzschild solution. We use this solution for explaining various
bound orbits around the black hole and eventually, as an immediate application,
in the spherical accretion flow around it.
