Transforming to the highly regular gauge for use in second-order self-force calculations

          @misc{ pirsa_PIRSA:21060041,
            doi = {10.48660/21060041},
            url = {https://pirsa.org/21060041},
            author = {Upton, Samuel},
            keywords = {Other},
            language = {en},
            title = {Transforming to the highly regular gauge for use in second-order self-force calculations},
            publisher = {Perimeter Institute},
            year = {2021},
            month = {jun},
            note = {PIRSA:21060041 see, \url{https://pirsa.org}}
          }
          

Abstract

With the publication of the first second-order self-force results, it has become even more clear of the need for fast and efficient calculations to avoid the computational expense encountered when using current methods in the Lorenz gauge. One ingredient for efficient calculation of second-order self-force data will be the use of the highly regular gauge (1703.02836 and 2101.11409) with its weaker divergences along the worldline of the small object. In this talk, we will present steps towards transforming the current Lorenz gauge data into the highly regular gauge to be used for quasicircular orbits in Schwarzschild spacetime. The end result will be a source that can be used as an input into the second-order Einstein equations (see talks by Andrew Spiers and Benjamin Leather). In particular, this will allow us to solve the second-order Teukolsky equation using a point particle source instead of requiring the use of a puncture scheme.