  In this paper, we present results obtained from our recent studies on the
location of the innermost stable circular orbit (ISCO) for binary neutron stars
(BNSs) in several levels of post Newtonian (PN) approximations. We reach the
following conclusion at present: (1) even in the Newtonian case, there exists
the ISCO for binary of sufficiently stiff equation of state (EOS). If the mass
and the radius of each star are fixed, the angular velocity at the ISCO
$\Omega_{ISCO}$ is larger for softer EOS: (2) when we include the first PN
correction, there appear roughly two kinds of effects. One is the effect to the
self-gravity of each star of binary and the other is to the gravity acting
between two stars. Due to the former one, each star of binary becomes compact
and the tidal effect is less effective. As a result, $\Omega_{ISCO}$ tends to
be increased. On the other hand, the latter one has the property to destabilize
the binary orbit, and $\Omega_{ISCO}$ tends to be decreased. If we take into
account both effects, however, the former effect is stronger than the latter
one, and $\Omega_{ISCO}$ becomes large with increase of the 1PN correction: (3)
the feature mentioned above is more remarkable for softer EOS if the mass and
radius are fixed. This is because for softer EOS, each star has the larger
central density and is susceptible to the GR correction: (4) there has been no
self consistent calculation including all the 2PN effects and only exist
studies in which one merely includes the effect of the 2PN gravity acting
between two stars. In this case, the effect has the property to destabilize the
binary orbit, so that $\Omega_{ISCO}$ is always smaller than that for the
Newtonian case. If we include the PN effect of the self-gravity to each star,
$\Omega_{ISCO}$ will increase.

General Relativity and Quantum Cosmology