Can the supertranslation symmetry of radiating spacetimes affect angular momentum loss?
That was the question on my mind when I went to a workshop at Berkeley, California last winter. I knew that the supertranslations were a global aspect of the gravitational memory effect, which produces a net displacement between particles after passage of a gravitational wave. What I didn’t know, and learned from David Garfinkle at Berkeley, was that there was an electromagnetic analog of radiation memory, which produces a momentum kick on test charges after passage of a wave. Surprisingly, this result has apparently gone unnoticed in the lengthy history of treatises and experiments on electrodynamics, presumably because it was never looked for. It is a prize for general relativity that this electromagnetic effect has now been recognized, at least at the theoretical level, through the analog with the gravitational version.
My interest was in the global properties of radiation memory, which had also escaped
previous investigation. Gravitational radiation has a global decomposition analogous to the E and B mode decomposition of electromagnetic waves This mode decomposition corresponds to the even or odd parity of the sky pattern of the polarization of the radiation. The supertranslation freedom is related to the E mode component of the gravitational radiation memory. Curiously, but not well understood, I found that all the proposed sources for gravitational memory are of the E mode type.
This prompted an investigation of this global behavior in electromagnetic theory, where the analysis is much simpler. I was able to show that a realistic system of charges and currents can only give rise to E mode radiation memory.
The central issue in the recent BICEP2 experiment is the ability of primordial gravitational waves to create a B mode component to the cosmic microwave background. It stands to explore whether similar results hold for the gravitational effect on electromagnetic radiation memory. And it still remains unanswered whether angular momentum conservation can be effected by gravitational radiation memory.
It is peculiar that electromagnetic radiation memory has been overlooked and never directly measured. It is a generic property of systems which eject charged particles with escape velocity. I hope some experimentalist will take note of this.
Read the full article in Classical and Quantum Gravity:
Global aspects of radiation memory
2014 Class. Quantum Grav. 31 205003
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