  It is shown that Birkhoff's theorem for the general theory of relativity is
overcome in the $f(R)$-theory of gravitation. That means, the $f(R)$-theory of
gravitation, unlike Einstein's general theory of relativity, does not forbid
gravitational radiation from a spherically symmetric source (whether stationary
or non-stationary). As a consequence, in the $f(R)$-theory a spherically
symmetric gravitational deformation (e.g., collapse/expansion or pulsation)
could emit gravitational waves (of tensor- and scalar polarization modes), a
phenomenon impossible in the general relativity. A test model is examined and
it turns out that the gravitational radiation is strongest when the surface of
the deforming object is in the vicinity of the (modified) event horizon, even
suddenly flares up just outside the latter. In this letter, within the
$f(R)$-theory of gravitation, a gravitational wave equation and a formula for
the gravitational emission power are derived. These formulae, along with
searching for signals, can be used for the experimental test of the
$f(R)$-theory. In general, including the spherically symmetry case,
gravitational radiation of both tensor- and scalar polarization modes are
allowed, although under some circumstance the contribution of scalar modes is
strongly suppressed.
