  The gravitational wave memory effect is characterized by the permanent
relative displacement of a pair of initially comoving test particles that is
caused by the passage of a burst of gravitational waves. Recent research on
this effect has clarified the physical origin and the interpretation of this
gravitational phenomenon in terms of conserved charges at null infinity and
"soft theorems." In this paper, we describe a more general class of effects
than the gravitational wave memory that are not necessarily associated with
these charges and soft theorems, but that are, in principle, measurable. We
shall refer to these effects as persistent gravitational wave observables.
These observables vanish in non-radiative regions of a spacetime, and their
effects "persist" after a region of spacetime which is radiating. We give three
examples of such persistent observables, as well as general techniques to
calculate them. These examples, for simplicity, restrict the class of
non-radiative regions to those which are exactly flat. Our first example is a
generalization of geodesic deviation that allows for arbitrary acceleration.
The second example is a holonomy observable, which is defined in terms of a
closed loop. It contains the usual "displacement" gravitational wave memory;
three previously identified, though less well known memory effects (the proper
time, velocity, and rotation memories); and additional new observables.
Finally, the third example we give is an explicit procedure by which an
observer could measure a persistent effect using a spinning test particle. We
briefly discuss the ability of gravitational wave detectors (such as LIGO and
Virgo) to measure these observables.
