The Electromagnetic Christodoulou Memory Effect and its Application to
  Neutron Star Binary Mergers
  Gravitational waves are predicted by the general theory of relativity. It has
been shown that gravitational waves have a nonlinear memory, displacing test
masses permanently. This is called the Christodoulou memory. We proved that the
electromagnetic field contributes at highest order to the nonlinear memory
effect of gravitational waves, enlarging the permanent displacement of test
masses. In experiments like LISA or LIGO which measure distances of test
masses, the Christodoulou memory will manifest itself as a permanent
displacement of these objects. It has been suggested to detect the
Christodoulou memory effect using radio telescopes investigating small changes
in pulsar's pulse arrival times. The latter experiments are based on
present-day technology and measure changes in frequency. In the present paper,
we study the electromagnetic Christodoulou memory effect and compute it for
binary neutron star mergers. These are typical sources of gravitational
radiation. During these processes, not only mass and momenta are radiated away
in form of gravitational waves, but also very strong magnetic fields are
produced and radiated away. Moreover, a large portion of the energy is carried
away by neutrinos. We give constraints on the conditions, where the energy
transported by electromagnetic radiation is of similar or slightly higher order
than the energy radiated in gravitational waves or in form of neutrinos. We
find that for coalescing neutron stars, large magnetic fields magnify the
Christodoulou memory as long as the gaseous environment is sufficiently
rarefied. Thus the observed effect on test masses of a laser interferometer
gravitational wave detector will be enlarged by the contribution of the
electromagnetic field. Therefore, the present results are important for the
planned experiments.
