Supertranslation Invariance and Covariance of Lorentz Charges in General Relativity

Explore a comprehensive lecture on the "angular momentum problem" in general relativity and the quest for covariant and supertranslation-invariant formulas for the flux of angular momentum and other Lorentz charges in asymptotically flat spacetimes. Delve into three key challenges faced by existing solutions: the implications of supertranslation-invariance and covariance on spacetime translation invariance, the dependence of flux on redundant auxiliary degrees of freedom, and the inability of supertranslation-invariant Lorentz charges to generate expected transformations of the Bondi mass aspect. Discover new, covariant formulas for fluxes that explicitly address the choice of reference frame underlying current literature's seemingly unambiguous results. This talk, part of the Thematic Programme on "Carrollian Physics and Holography" at the Erwin Schrödinger International Institute for Mathematics and Physics, offers a deep dive into advanced concepts in theoretical physics and general relativity.