Energy extraction from boosted black holes: Penrose process, jets, and the membrane at infinity

Numerical simulations indicate that black holes carrying linear momentum and/or orbital momentum can power jets. The jets extract the kinetic energy stored in the black hole's motion. This could provide an important electromagnetic counterpart to gravitational wave searches. We develop the theory underlying these jets. In particular, we derive the analogues of the Penrose process and the Blandford-Znajek jet power prediction for boosted black holes. The jet power we find is $(v/2M)^2 \Phi^2/(4\pi)$, where $v$ is the hole's velocity, $M$ is its mass, and $\Phi$ is the magnetic flux. We show that energy extraction from boosted black holes is conceptually similar to energy extraction from spinning black holes. However, we highlight two key technical differences: in the boosted case, jet power is no longer defined with respect to a Killing vector, and the relevant notion of black hole mass is observer dependent. We derive a new version of the membrane paradigm in which the membrane lives at infinity rather than the horizon and we show that this is useful for interpreting jets from boosted black holes. Our jet power prediction and the assumptions behind it can be tested with future numerical simulations.