https://doi.org/10.1140/epjp/s13360-025-06516-5
Regular Article
Displacement memory effect from supersymmetry
1
Department of Physics, Istanbul University, 34134, Istanbul, Turkey
2
Department of Energy Systems Engineering, Istanbul Bilgi University, 34060, Istanbul, Turkey
3
Department of Physics, Bogazici University, 34342, Bebek, Istanbul, Turkey
4
Feza Gursey Center for Physics and Mathematics, Bogazici University, 34684, Kandilli, Istanbul, Turkey
a
mahmut.elbistan@bilgi.edu.tr
Received:
28
May
2025
Accepted:
2
June
2025
Published online:
16
June
2025
We explain the recent results on the displacement memory effect (DME) of plane gravitational waves using supersymmetric quantum mechanics. This novel approach stems from that both the geodesic and the Schrödinger equations are Sturm-Liouville boundary value problems. Supersymmetry provides a unified framework for the Pöschl-Teller and the Scarf profiles and yields the critical values of the associated wave amplitudes for DME in a natural way. Within our framework, we obtain a compact formula for DME in terms of the asymptotic values of the superpotential and the geodesics. In addition, this new technique enables us to build plane and gravitational waves with 2-transverse directions using superpartner potentials. Lastly, we study DME within a singular wave profile inspired by supersymmetric quantum mechanics, which demonstrates the broader applicability of our method.
© The Author(s) 2025
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