High-speed black-hole encounters and gravitational radiation

Encounters between black holes are considered in the limit that the approach velocity tends to the speed of light. At high speeds, the incoming gravitational fields are concentrated in two plane-fronted shock regions, which become distorted and deflected as they pass through each other. The structure of the resulting curved shocks is analyzed in some detail, using perturbation methods. This leads to calculations of the gravitational radiation emitted near the forward and backward directions. These methods can be applied when the impact parameter is comparable to $G{c}^{-2\mathrm{}}M{\gamma }^2$ where $M$ is a typical black-hole mass and $\gamma$ is a typical Lorentz factor (measured in a center-of-mass frame) of an incoming black hole. Then the radiation carries power/solid angle of the characteristic strong-field magnitude $c^5{G}^{-1\mathrm{}}$ within two beams occupying a solid angle of order ${\gamma }^{-2\mathrm{}}$. But the methods are still valid when the black holes undergo a collision or close encounter, where the impact parameter is comparable to $G{c}^{-2\mathrm{}}M\gamma$. In this case the radiation is apparently not beamed, and the calculations describe detailed structure in the radiation pattern close to the forward and backward directions. The analytic expressions for strong-field gravitational radiation indicate that a significant fraction of the collision energy can be radiated as gravitational waves.