The Spin Memory Effect

When a burst of gravitational radiation passes through a region of spacetime it leaves behind a permanent trace — a memory encoded in the geometry itself. The most celebrated instance is the displacement memory effect (Zel'dovich & Polnarev 1974; Christodoulou 1991): free test particles end up permanently displaced after the wave train has passed.

In 2016 Pasterski, Strominger, and Zhiboedov identified a companion effect at subleading order in the $1/r$ expansion — the spin memory effect. Rather than displacing test particles, it imparts a permanent change to the time-integrated velocity circulation around a closed curve encircling the source: a gravitational holonomy. Its physical source is the angular momentum carried away by gravitational waves, and its mathematical home is the super-rotation sector of the BMS asymptotic symmetry group.

This module develops the spin memory effect from first principles, using the Bondi–Sachs formalism and the language of null infinity $\mathscr{I}^+$.