Buchdahl-Bondi limit in modified gravity: Packing extra effective mass in relativistic compact stars

We generalize the Buchdahl–Bondi limit for the case of static, spherically symmetric, relativistic compact stars immersed in Schwarzschild vacuum in the $f(R)$-theory of gravity, subject to very generic regularity, thermodynamic stability, and matching conditions. Similar to the case of general relativity, our result is model independent and remains true for any physically realistic equation of state of standard stellar matter. We show that an extramassive stable star can exist in these theories, with a surface redshift larger than 2, which is forbidden in general relativity. This result gives a novel and interesting observational test for validity or otherwise of general relativity and also provides a possible solution to the dark matter problem.