Strong-field scattering of two black holes: Numerics versus analytics

We probe the gravitational interaction of two black holes in the strong-field regime by computing the scattering angle. of hyperboliclike, close binary-black-hole encounters as a function of the impact parameter. The fully general-relativistic result from numerical relativity is compared to two analytic approximations: post-Newtonian theory and the effective-one-body formalism. As the impact parameter decreases, so that black holes pass within a few times their Schwarzschild radii, we find that the post-Newtonian prediction becomes quite inaccurate, while the effective-one-body one keeps showing a good agreement with numerical results. Because we have explored a regime which is very different from the one considered so far with binaries in quasicircular orbits, our results open a new avenue to improve analytic representations of the general-relativistic two-body Hamiltonian.