Synergistic approach to the two-body problem in General Relativity: black-hole binaries in the intermediate mass-ratio regime

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This project tackles the problem of modelling the dynamics and gravitational-wave signature of black-hole insiprals in intermediate mass-ratio regime (1:100 - 1:1000). For more extreme mass ratios, black hole perturbation theory provides a sufficient description, whilst in the case of comparable masses numerical relativity has been very successful. But neither works well when the mass ratio is intermediate. Since current and future gravitational-wave experiments are not unlikely to observe such intermediate mass-ratio inspirals, their modelling remains an important open problem in gravitational-wave physics. In this project we propose to tackle the problem through a combination of black-hole perturbation and numerical relativistic techniques. The research will be done in collaboration with the leading numerical-relativity group at the Albert Einstein Institute (Max Planck Institute for Gravitational Physics) in Germany. The idea is to construct a sufficiently accurate solution of the full Einstein Field Equations for the binary's spacetime by matching an approximate analytical solution near the small object to a fully nonlinear numerical solution elsewhere. In effect, a region near the small object is ``excised'', with excision boundary conditions derived analytically using perturbative methods. The effect will be to partially relieve the scale disparity that impedes the efficiency of the numerical calculation. We plan to begin by studying a relatively simple linear scalar-field model in 1+1 dimensions. Once we are confident that our excision procedure works well, we will endeavourer to apply a similar strategy to the gravitational problem in 3+1 dimensions, at which stage we will collaborate with the AEI group. The plan is to incorporate our new excision method into the existing SpEC platform (which already produces accurate waveforms for the LIGO-Virgo Collaboration, currently for mass ratios up to ~1:10).