Surface configuration in $R+{\mu }^4\mathrm{/}R$ gravity

We investigate the conditions on the additional constant $\mu$ in the so-called $R+{\mu }^4\mathrm{/}R$ 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.