Time-domain metric reconstruction for hyperbolic scattering

          @misc{ pirsa_PIRSA:21060058,
            doi = {10.48660/21060058},
            url = {https://pirsa.org/21060058},
            author = {Long, Oliver},
            keywords = {Other},
            language = {en},
            title = {Time-domain metric reconstruction for hyperbolic scattering},
            publisher = {Perimeter Institute},
            year = {2021},
            month = {jun},
            note = {PIRSA:21060058 see, \url{https://pirsa.org}}
          }
          

Abstract

Hyperbolic-type scattering orbits are excellent probes of the strong-field regime around black holes, and their analysis can inform the construction of an accurate two-body Hamiltonian. In particular, it has been shown that knowledge of the scattering angle through linear order in the mass ratio completely determines the 4PM Hamiltonian. With this motivation in mind, we describe a technique for (numerical) self-force calculations that can efficiently tackle scatter orbits. The method is based on a time-domain metric reconstruction from a Hertz potential in a radiation gauge. The crucial ingredient in this formulation are certain jump conditions that (each multipole mode of) the Hertz potential must satisfy along the orbit, in a 1+1-dimensional multipole reduction of the problem. We show a closed-form expression for these jumps, for an arbitrary geodesic orbit in Schwarzschild spacetime, and present a full numerical implementation for a scatter orbit.