  We prove that for spacetimes solving the Einstein-Maxwell (EM) equations, the
electromagnetic field contributes at highest order to the nonlinear memory
effect of gravitational waves. In [5] D. Christodoulou showed that
gravitational waves have a nonlinear memory. He discussed how this effect can
be measured as a permanent displacement of test masses in a laser
interferometer gravitational wave detector. Christodoulou derived a precise
formula for this permanent displacement in the Einstein vacuum (EV) case. We
prove in Theorem 6 that for the EM equations this permanent displacement
exhibits a term coming from the electromagnetic field. This term is at the same
highest order as the purely gravitational term that governs the EV situation.
On the other hand, in Chapter 3, we show that to leading order, the presence of
the electromagnetic field does not change the instantaneous displacement of the
test masses. Following the method introduced by D. Christodoulou in [5] and
asymptotics derived by N. Zipser in [8] and [9], we investigate gravitational
radiation at null infinity in spacetimes solving the EM equations. We study the
Bondi mass loss formula at null infinity derived in [9]. We show that the mass
loss formula from [9] is compatible with the one in Bondi coordinates obtained
in [4]. And we observe that the presence of the electromagnetic field increases
the total energy radiated to infinity up to leading order. Moreover, we compute
the limit of the area radius at null infinity in Theorem 7.
