We report on the first fully consistent conventional cluster simulation
which includes terms up to post5/2 Newtonian in the potential of
the massive body. Numerical problems for treating extremely energetic
binaries orbiting a single massive object are circumvented by employing the
special "wheel-spoke" regularization method of Zare (1974) which has not
been used in large-N simulations before. Idealized models containing
N = 105 particles of mass 1 M(sun) with a central black hole of 300 M(sun)
have been studied on GRAPE-type computers. An initial half-mass radius of
rh = 0.1 pc is sufficiently small to yield examples of relativistic
coalescence. This is achieved by significant binary shrinkage within a
density cusp environment, followed by the generation of extremely high
eccentricities which are induced by Kozai (1962) cycles and/or resonant
relaxation. More realistic models with white dwarfs and ten times larger
half-mass radii also show evidence of GR effects before disruption.
Experimentation with the post-Newtonian terms suggests that reducing
the time-scales for activating the different orders progressively may be
justified for obtaining qualitatively correct solutions without aiming
for precise predictions of the final gravitational radiation wave form.
The results obtained suggest that the standard loss-cone arguments
underestimate the swallowing rate in globular clusters containing a
central black hole.