  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.

General Relativity and Quantum Cosmology;High Energy Physics - Theory