Research Theme: Extended BMS Algebra, Spin and CenterofMass Memory Effects
This post summarizes three papers related to the conserved quantities of an extension of the BondiMetznerSachs (BMS) group and two related new memory effects.
Papers Highlighted

D. A. Nichols. “Centerofmass angular momentum and memory effect in asymptotically flat spacetimes.” Phys. Rev. D 98, 064032 (2018), arXiv:1807.08767.

D. A. Nichols. “Spin memory effect for compact binaries in the postNewtonian approximation.” Phys. Rev. D 95, 084048 (2017), arxiv:1702.03300.

E. E. Flanagan and D. A. Nichols. “Conserved charges of the extended BondiMetznerSachs algebra.” Phys. Rev. D 95, 044002 (2017), arxiv:1510.03386.
Summary of the Papers
The BondiMetznerSachs (BMS) group is the symmetry group of asymptotically flat spacetimes, and it consists of the Lorentz transformations and the supertranslations (an infinitedimensional commutative group that has the spacetime translations as a subgroup). There recently was a proposal that a larger symmetry algebra than the BMS algebra could be relevant. This new algebra was called the extended BMS algebra, and it included the infinite number of conformal Killing vectors on the twosphere, not just the smooth sixparameter family of Lorentz transformations. We computed the conserved quantities corresponding to these new symmetries in a somewhat more general context than before, and we found that they are finite and that they have an electric and a magneticparity part. These two parts are generalizations of the spin angular momentum and the centerofmass parts of the relativistic angular momentum (the superspin and supercenterofmass charges, respectively). The change in the superspin charges can be a source of a new kind of memory effect, which had been proposed earlier, called the spin memory effect.
Another source of the spin memory effect is the effective angular momentum per solid angle that is radiated in gravitational waves. I recently computed the expansion of this effective angular momentum flux in terms of radiative moments of the gravitationalwave strain, thereby deriving a quadrupolelike formula for the spin memory. I then specialized to compact binary sources in the postNewtonian approximation. In this limit, I found that the spin memory has a substantial slow secular growth during the inspiral stage of a compact binary. In addition, the rate of accumulation of the spin memory is related to a nonhereditary, nonlinear, and nonoscillatory contribution to the gravitational waveform that appears at a high order in the postNewtonian expansion. This rate of accumulation of the spin memory might be detectable by thirdgeneration gravitationalwave detectors, such as the Einstein Telescope, by coherently adding the spin memory signals from hundreds of gravitationalwave observations of blackholebinary mergers.
I also showed that changes in the supercenterofmass charges can also produce a new type of memory effect, which I called the centerofmass memory effect. Like the spin memory effect, it produces a lasting change in a quantity related to the time integral of the gravitationalwave strain. There are terms in the gravitational waves related to the centerofmass memory effect. These gravitationalwave terms, however, will be weaker than those related to the spin memory effect. As a result, it is less likely that the next generation of gravitationalwave detectors will be able to find evidence for the effect. It should, however, appear in the postNewtonian expansion of the gravitational waveform, when the gravtiational waveform is computed at fourth postNewtonian order.