We report on the first fully consistent conventional cluster simulation which includes terms up to { post } ^ { 5 / 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 = 1 \times 10 ^ { 5 } particles of mass 1 ~ { } { M } _ { \odot } with a central black hole of 300 ~ { } { M } _ { \odot } have been studied on GRAPE-type computers .
An initial half-mass radius of r _ { h } \simeq 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 .