  From time to time, different observations suggest that Einstein's theory of
general relativity (GR) may not be the ultimate theory of gravity. Various
researchers have suggested that the $f(R)$ theory of gravity is the best
alternative to replace GR. Using $f(R)$ gravity, one can elucidate the various
unexplained physics of compact objects, such as black holes, neutron stars, and
white dwarfs. Researchers have already put effort into finding the vacuum
solution around a black hole in $f(R)$ gravity. However, for a long time, they
could not find an asymptotically flat vacuum solution. In this article, we show
that the asymptotically flat vacuum solution of $f(R)$ gravity is possible and
thereby use it to explain the spherical accretion flow around the black hole.
