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Résumé |
pp-waves are the simplest (and the first obtained) non-linear radiative solution
in general relativity. The realization of memory effects induced by vacuum
gravitational plane wave (VGPW) (a specific subset of pp-waves) on a couple of
test particles has been extensively study (https://arxiv.org/abs/1704.05997,
https://arxiv.org/abs/1705.01378, https://arxiv.org/abs/1803.09640). So far, the
work has focused on the velocity memory effect and until recently, it was believed
that no displacement memory could be realized in such radiative geometry. In this
talk, I will show that both displacement and velocity memories can be induced by a
VGPW and I will present the first general classification for the conditions under
which this happens. This classification holds for both pulse and step profiles
(the latter case being the standard ad hoc model for implementing memory
contribution to the waveform profile. See https://arxiv.org/abs/1108.3121) and
allows to understand the numerical examples presented recently in
https://arxiv.org/abs/2405.12928. Along the way, I will review several key results
to analyze the geodesic motion and geodesic deviation equation in VGPW, and in
particular the explicit and hidden symmetries of these geometries. I will further
show that polarized VGPW enjoys a new type of symmetry under Möbius
reparametrization of the null time (which turns out to be a more general property
inherent to any null hypersurface). I will also review some theorems relating
hidden symmetries (under Killing tensors) and the solution space of the geodesic
deviation equation used to identify the memory effects. This talk is based on the
recent article: https://inspirehep.net/literature/2796995 |
