Geodesic congruences in exact plane wave spacetimes and the memory effect

Understand

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.