  In the near future, gravitational wave detection is set to become an
important observational tool for astrophysics. It will provide us with an
excellent means to distinguish different gravitational theories. In effective
form, many gravitational theories can be cast into an f(R) theory. In this
article, we study the dynamics and gravitational waveform of an equal-mass
binary black hole system in f(R) theory. We reduce the equations of motion in
f(R) theory to the Einstein-Klein-Gordon coupled equations. In this form, it is
straightforward to modify our existing numerical relativistic codes to simulate
binary black hole mergers in f(R) theory. We considered binary black holes
surrounded by a shell of scalar field. We solve the initial data numerically
using the Olliptic code. The evolution part is calculated using the extended
AMSSNCKU code. Both codes were updated and tested to solve the problem of
binary black holes in f(R) theory. Our results show that the binary black hole
dynamics in f(R) theory is more complex than in general relativity. In
particular, the trajectory and merger time are strongly affected. Via the
gravitational wave, it is possible to constrain the quadratic part parameter of
f(R) theory in the range |a_2|<10^{11} m^2 . In principle, a gravitational wave
detector can distinguish between a merger of binary black hole in f(R) theory
and the respective merger in general relativity. Moreover, it is possible to
use gravitational wave detection to distinguish between f(R) theory and a non
self-interacting scalar field model in general relativity.
