Center-of-mass ambiguity for Bondi-Metzner-Sachs charges
Adam D. Helfer
TL;DR
This paper reveals an infinite-dimensional ambiguity in defining the center of mass and spin within the BMS charge framework in general relativity, challenging previous assumptions and highlighting the complexity of these concepts.
Contribution
It identifies a previously unnoticed ambiguity in the natural definitions of center of mass and spin in the BMS charge approach to angular momentum in general relativity.
Findings
Center-of-mass definition has an infinite-dimensional ambiguity.
Spin is translation-invariant but not supertranslation-invariant.
Previous work overlooked this ambiguity due to implicit assumptions.
Abstract
Dray and Streubel proposed a definition of angular momentum in general relativity based on `Bondi-Metzner-Sachs (BMS) charges'. I show here that the natural definition of center of mass in this program has an infinite-dimensional ambiguity. (This seems not to have been noticed before because previous work has tacitly carried over a special-relativistic assumption.) A related point is that the natural definition of spin in this context is translation-, but not supertranslation-, invariant.
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