Geodesic congruences in exact plane wave spacetimes and the memory effect

Abstract

Displacement and velocity memory effects in the exact, vacuum, plane gravitational wave line element have been studied recently by looking at the behaviour of pairs of geodesics or via geodesic deviation. Instead, one may investigate the evolution of geodesic congruences. In our work here, we obtain the evolution of the kinematic variables which characterise timelike geodesic congruences, using chosen pulse profiles (square and sech-squared) in the exact, plane gravitational wave line element. We also analyse the behaviour of geodesic congruences in possible physical scenarios describable using derivatives (first, second and third) of one of the chosen pulses. Beginning with a discussion on the generic behaviour of such congruences and consequences thereof, we find exact analytical expressions for shear and expansion with the two chosen pulse profiles. Qualitatively similar numerical results are noted when various derivatives of the sech-squared pulse are used. We conclude that for geodesic congruences, a growth (or decay) of shear causes focusing of an initially parallel congruence, after the departure of the pulse. A correlation between the `focusing time (or $u$ value, $u$ being the affine parameter)' and the amplitude of the pulse (or its derivatives) is found. Such features distinctly suggest a memory effect, named in recent literature as $\mathcal{B}$ memory.

arXiv comment27 pages, 13 figures, major changes (including title and abstract), rewritten with a different focus, new results added

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• Conserved charges in Chern-Simons modified theory and memory effects
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• Memory effects in Kundt wave spacetimes
• Entanglement harvesting for different gravitational wave burst profiles with and without memory
• Memory effect and BMS symmetries for extreme black holes
• A simple analytic example of the gravitational wave memory effect
• Displacement within velocity effect in gravitational wave memory
• Displacement memory effect near the horizon of black holes
• Kundt wave geometries in Eddington-inspired Born-Infeld gravity: New solutions and memory effects
• Memory Effect of Gravitational Wave Pulses in PP-Wave Spacetimes
• Gravitational wave memory and its effects on particles and fields
• Displacement Memory Effect from Supersymmetry
• Flyby-induced displacement: analytic solution
• Gravitational wave pulse and memory effects for hairy Kiselev black hole and its analogy with Bondi-Sachs formalism
• Test gravitational waves in sandwich wave background
• Gravitational memory meets astrophysical environments: exploring a new frontier through osculations
• Gravitational wave memory in wormhole spacetimes