  We obtain an infinite number of exact static, Ricci-flat spherically
symmetric vacuum solutions for a class of f(R) theories of gravity. We
analytically derive two exact vacuum black-hole solutions for the same class of
f(R) theories. The two black-hole solutions have the event-horizon at the same
point; however, their asymptotic features are different. Our results suggest
that no-hair theorem may not hold for generic modified gravity theories. We
discuss the implications of our work to distinguish modified gravity theories
from general relativity in gravitational wave detections.
