  It is well-known that there is no spherical/topologically spherical
gravitational waves in vacuum space in general relativity. We show that a
deviation from general relativity leads to exact vacuum spherical gravitational
waves, no matter how tiny this deviation is. We also discuss the related
topics, including Vaidya-like metric in $f(R)$ gravity. We demonstrate that the
existence of spherical gravitational wave is a non perturbative property for
gravities. We investigate energy carried by this nonperturbative wave. We first
find the wave solution from investigations of Vaidya-like metric in $f(R)$
gravity, which has only one longitude polarization. We further extend it to a
metric with two transverse polarizations by directly solving the field
equation.
