Displacement Memory Effect from Supersymmetry

Abstract

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.

Published version, 17 pages

References in corpus (17)

• Celestial Mechanics, Conformal Structures, and Gravitational Waves
• The Kerr-Schild double copy in curved spacetime
• Supersymmetry in Quantum Mechanics
• Detecting the gravitational wave memory effect with TianQin
• Scaling and conformal symmetries for plane gravitational waves
• Memory effect, conformal symmetry and gravitational plane waves
• Geodesic congruences in exact plane wave spacetimes and the memory effect
• Self-isospectral tri-supersymmetry in PT-symmetric quantum systems with pure imaginary periodicity
• Memory effects in Kundt wave spacetimes
• Niederer's transformation, time-dependent oscillators and polarized gravitational waves
• Displacement within velocity effect in gravitational wave memory
• Displacement memory effect near the horizon of black holes
• Particle motion in circularly polarized vacuum pp waves
• "Kepler Harmonies" and conformal symmetries
• Memory Effect and Carroll Symmetry: 50 years later
• Lukash plane waves, revisited
• Neutron-proton scattering and singular potentials

Cited by in corpus (1)

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