  Numerical simulations of binary neutron stars by Wilson, Mathews, and
Marronetti indicated that neutron stars that are stable in isolation can be
made to collapse to black holes when placed in a binary. This claim was
surprising as it ran counter to the Newtonian expectation that a neutron star
in a binary should be more stable, not less. After correcting an error found by
Flanagan, Wilson and Mathews found that the compression of the neutron stars
was significantly reduced but not eliminated. This has motivated us to ask the
following general question: Under what circumstances can general-relativistic
tidal interactions cause an otherwise stable neutron star to be compressed? We
have found that if a nonrotating neutron star possesses a current-quadrupole
moment, interactions with a gravitomagnetic tidal field can lead to a
compressive force on the star. If this current quadrupole is induced by the
gravitomagnetic tidal field, it is related to the tidal field by an
equation-of-state-dependent constant called the gravitomagnetic Love number.
This is analogous to the Newtonian Love number that relates the strength of a
Newtonian tidal field to the induced mass quadrupole moment of a star. The
compressive force is almost never larger than the Newtonian tidal interaction
that stabilizes the neutron star against collapse. In the case in which a
current quadrupole is already present in the star (perhaps as an artifact of a
numerical simulation), the compressive force can exceed the stabilizing one,
leading to a net increase in the central density of the star. This increase is
small (<~1%) but could, in principle, cause gravitational collapse in a star
that is close to its maximum mass.
