Lorenz-gauge reconstruction for Teukolsky solutions with sources in electromagnetism

          @misc{ pirsa_PIRSA:21060044,
            doi = {10.48660/21060044},
            url = {https://pirsa.org/21060044},
            author = {Green, Stephen},
            keywords = {Other},
            language = {en},
            title = {~Lorenz-gauge reconstruction for Teukolsky solutions with sources in electromagnetism},
            publisher = {Perimeter Institute},
            year = {2021},
            month = {jun},
            note = {PIRSA:21060044 see, \url{https://pirsa.org}}
          }
          

Abstract

Reconstructing a metric or vector potential that corresponds to a given solution to the Teukolsky equation is an important problem for self-force calculations. Traditional reconstruction algorithms do not work in the presence of sources, and they give rise to solutions in a radiation gauge. In the electromagnetic case, however, Dolan (2019) and Wardell and Kavanagh (2020) very recently showed how to reconstruct a vector potential in Lorenz gauge, which is more convenient for self-force. Their algorithm is based on a new Hertz-potential 2-form. In this talk, I will first show that the electromagnetic Teukolsky formalism takes a simplified form when expressed in terms of differential forms and the exterior calculus. This formalism makes the new Lorenz-gauge construction much more transparent, and it enables an extension to nonzero sources. In particular, I will derive a corrector term, related to the charge current, which when added to the vector potential gives a solution to the Maxwell equations with nonzero source. I will conclude by discussing prospects for extending to the gravitational case.