  We analytically study the properties of the electromagnetic field in vacuum
around close binary compact stars containing at least one neutron star. We show
that the orbital motion of the neutron star induces high multipole modes of the
electromagnetic field just before the merger. These modes are superimposed to
form a spiral arm configuration and its edge is found to be a likely site for
magnetic reconnection. These modes also enhance the total Poynting flux from
neutron star binaries by a factor of 2--4. We also indicate that the electric
field induced by the orbital motion lead to a magnetosphere around binaries and
estimate its plasma density, which has a different parameter dependence than
Goldreich-Julian density. With these properties, we discuss possible
electromagnetic counterparts to gravitational wave events, and identify radio
precursors, such as fast radio bursts, as the most promising observational
targets.
