Numerical Relativity on Constant Mean Curvature Hypersurfaces

          @misc{ pirsa_PIRSA:11100089,
            doi = {10.48660/11100089},
            url = {https://pirsa.org/11100089},
            author = {Bardeen, James},
            keywords = {Strong Gravity},
            language = {en},
            title = {Numerical Relativity on Constant Mean Curvature Hypersurfaces},
            publisher = {Perimeter Institute},
            year = {2011},
            month = {oct},
            note = {PIRSA:11100089 see, \url{https://pirsa.org}}
          }
          

Abstract

Constant mean curvature (uniform K) hypersurfaces extend to future null infinity in asymptotically flat spacetimes. With conformal compactification, the entire hypersurface can be covered by a finite spatial grid, eliminating any need an "outgoing wave" boundary condition or for extrapolation to find gravitational wave amplitudes. I will discuss the asymptotic behavior near future null infinity, how this can be simplified by suitable gauge conditions, and how this determines the physical Bondi energy and momentum of the system. Numerical results for how Bowen-York parameters in the conformally flat initial value problem are related to the physical energy and momentum in systems with single and binary black holes will be presented.