Memory effect of massive gravitational waves
Memory effect for gravitational waves was first discovered by Zel'dovich and Polnarev, originally, conclusion of their paper is that test masses initially at rest will suffer permanent displacement after the passage of a gravitational wave. Afterwards, Bondi and Pirani as well as Grishchuk and Polnarev arrived at a different conclusion in their analysis. Namely, they concluded that passage of a gravitational wave will be encoded, not in permanent displacement but, in non-zero relative velocity of test masses. Recently, Zhang et al analyzed this problem too and, among other things, concluded that velocity, and not displacement, memory effect happens for the case of plane gravitational waves and that is connected with soft gravitons.
Unrelated, at first sight, investigation of asymptotic symmetries at null infinity gave some unexpected results which connected asymptotic symmetries, soft theorems and displacement memory effect. This line of reasoning is applied on black holes by Hawking et al, and offered new insights into black hole physics. More precise, they derived that black holes have infinite number of additional soft charges which highly constrain their dynamics. Importance of this insight is still under investigation, just to mention that Afshar et al, using this idea, constructed microstates of three dimensional black holes.
Because all the analysis, of previously mentioned works, is done in the framework of general relativity it is not clear are soft gravitons the essential component for the validness of the obtained results.
In this talk we review the analysis of the geodesic motion in asymptotically flat plane wave space-time first in three dimensions for theory that has no mass-less degrees of freedom and second in four dimensional space-time but for the case of massive gravitational waves. We discover the presence of velocity memory effect in both cases. Without a doubt, we can conclude that no soft particles are needed for the memory effect. Immediate, implications of this on a relation of asymptotic symmetries and soft theorems is not clear and requires further investigation.