New spin-orbit and spin-squared post-Newtonian results from first-order self-force

          @misc{ pirsa_PIRSA:21060025,
            doi = {10.48660/21060025},
            url = {https://pirsa.org/21060025},
            author = {Khalil, Mohammed},
            keywords = {Other},
            language = {en},
            title = {New spin-orbit and spin-squared post-Newtonian results from first-order self-force},
            publisher = {Perimeter Institute},
            year = {2021},
            month = {jun},
            note = {PIRSA:21060025 see, \url{https://pirsa.org}}
          }
          

Abstract

The scattering angle function exhibits a simple dependence on the mass ratio, which has been recently used to obtain new post-Newtonian (PN) results for arbitrary mass ratios from first-order self-force calculations. In this talk, I will present results for the spin-orbit coupling at fourth subleading PN order (5.5PN), including both local and nonlocal contributions, and the spin-squared coupling at third subleading PN order (5PN) for aligned spins. The spin-orbit results are missing one coefficient at second order in the mass ratio, and the spin-squared results are missing one coefficient at first order in the mass ratio. The latter could be determined from a self-force calculation of the spin-precession invariant for circular orbits in Schwarzschild to linear order in the spin of the small object. I will also discuss implications regarding the first law of binary mechanics with spin quadrupole and its relation to tidal invariants.