  We investigate the gravitational energy-momentum distribution in the
space-time of two black holes in circular orbit, in the context of the
teleparallel equivalent of general relativity. This field configuration is
important because gravitational waves are expected to be emitted in the final
stages of inspiral and merger of binary black holes. We address an approximate
solution of Einstein's field equations that describes two non-spinning black
holes that circle each other in the $xy$ plane, obtain the total energy of the
space-time and verify that the gravitational binding energy is negative. We
show that gravitational radiation is emitted as long as the separation between
the holes decreases in time. If the black holes are spinning and circle each
other, it has been found in the literature that, during the pre-merger
inspiral, they bob up and down sinusoidally. The understanding of this
phenomenon requires the understanding of the gravitational energy-momentum flow
in the space-time of binary black holes. For the time dependent metric tensor
of a general binary black hole system, the non-vanishing of the gravitational
momentum may explain the bobbing of spinning black holes.
