  We investigate the conditions on the additional constant $\mu$ in the
so-called $R+\mu^4/R$ theory of gravity, due to existence of different kinds of
space-like surfaces in both weak field and strong field limits, and their
possible correspondence to black hole event horizons. Adopting a Schwarzschild
limit, we probe the behaviour of $\mu$ in different contexts of radial and
radial-rotational congruence of null geodesics. We show that these cases serve
as correspondents to black hole horizons in some peculiar cases of study.
