  Binary mergers involving black holes and neutron stars have been proposed as
major sources of gravitational waves, r--process nucleosynthesis, and gamma ray
bursters. In addition, they represent an important, and possibly unique,
observable that could distinguish between normal and self--bound neutron stars.
These two families of stars have distinctly different mass--radius
relationships resulting from their equations of state which can be revealed
during their mergers if stable mass transfer ensues. We consider two cases of
gravitational-radiation induced binary mergers: (i) a black hole and a normal
neutron star, and (ii) a black hole and a self-bound strange quark matter star.
We extend previous Newtonian analyses to incorporate the pseudo-general
relativistic Paczy\'nski-Wiita potential or a potential correct to
second--order post-Newtonian order in Arnowitt--Deser--Misner coordinates.
These potentials are employed to study both the orbital evolution of the binary
and the Roche lobe geometry that determines when and if stable mass transfer
between the components is possible. The Roche lobe geometry with pseudo-general
relativistic or post-Newtonian potentials has not heretofore been considered.
Our analysis shows that differences in the evolution of normal neutron stars
and strange quark matter stars are significant and could be detected in gravity
waves. Both the amplitude and frequencies of the wave pattern are affected. In
addition, details of the equation of state for either normal neutron stars or
strange quark stars may be learned. A single merger could reveal one or two
individual points of the mass-radius relation, and observations of several
mergers could map a significant portion of this relation.
