arXiv:2003.05139v1 [gr-qc] 11 Mar 2020 Infinitely degenerate exact vacuum solutions in f (R) gravity Semin Xavier, 1, ∗ Jose Mathew, 2, † and S. Shankaranarayanan 1, ‡ 1 Department of Physics, Indian Institute of Technology, Mumbai, Maharashtra 400076 2 Department of Physics, The Cochin College, Kochi, Kerala, India Abstract We obtain an infinite number of exact static 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 point that the Birkhoff theorem is not valid for all modified gravity theories. We discuss the implications of our work to distinguish modified gravity theories from general relativity in gravitational wave detections. * seminxavier@iitb.ac.in † josecherukara@gmail.com ‡ shanki@phy.iitb.ac.in 1