  The gravitational analog of the electromagnetic Poynting vector is
constructed using the field equations of general relativity in the Hilbert
gauge. It is found that when the gravitational Poynting vector is applied to
the solution of the linear mass quadrupole oscillator, the correct
gravitational quadrupole radiation flux is obtained. Further to this, the
Maxwell-like gravitational Poynting vector gives rise to Einstein's quadrupole
radiation formula. The gravitational energy-momentum (pseudo) tensor obtained
is symmetric and traceless. The former property allows the definition of
angular momentum for the free gravitational field.
