  We investigate the Einstein vacuum equations as well as the Einstein-null
fluid equations describing neutrino radiation. We find new structures in
gravitational waves and memory for asymptotically-flat spacetimes of slow
decay. These structures do not arise in spacetimes resulting from data that is
stationary outside a compact set. Rather the more general situations exhibit
richer geometric-analytic interactions displaying the physics of these more
general systems. It has been known that for stronger decay of the data
gravitational wave memory is finite and of electric parity only. We investigate
general spacetimes that are asymptotically flat in a rough sense, where the
decay of the data to Minkowski space towards infinity is very slow. Main new
feature: We prove that there exists diverging magnetic memory sourced by the
magnetic part of the curvature tensor (a) in the Einstein vacuum and (b) in the
Einstein-null-fluid equations. The magnetic memory occurs naturally in the
Einstein vacuum setting (a) of pure gravity. In case (b), in the ultimate class
of solutions, the magnetic memory also contains a curl term from the
energy-momentum tensor for neutrinos also diverging at the highest rate. The
electric memory diverges too, it is generated by the electric part of the
curvature tensor and in the Einstein-null-fluid situation also by the
corresponding energy-momentum component. In addition, we find a panorama of
finer structures in these manifolds. Some of these manifest themselves as
additional contributions to both electric and magnetic memory. Our theorems
hold for any type of matter or energy coupled to the Einstein equations as long
as the data decays slowly towards infinity and other conditions are satisfied.
The new results have many applications ranging from mathematical general
relativity to gravitational wave astrophysics, detecting dark matter and other
topics in physics.
