On the rarity of rocket-driven Penrose extraction in Kerr spacetime
This addresses the feasibility of energy extraction from black holes for theoretical physics and potential space applications, but it is incremental as it focuses on specific conditions and protocols.
The paper tackled the problem of rocket-driven Penrose extraction in Kerr spacetime, finding that extraction with escape is rare (at most ~1% in broad scans) but can reach ~70% success under optimal tuning with high black-hole spin and relativistic exhaust.
We study rocket-driven Penrose extraction in the test-particle limit on a fixed Kerr background for equatorial prograde flybys under explicit steering prescriptions. A spacecraft ejects exhaust inside the ergosphere; when the exhaust attains negative Killing energy, the remaining spacecraft gains energy by 4-momentum conservation. Across 320{,}000 simulated trajectories spanning black-hole spin, exhaust velocity, and orbital parameters, extraction with escape is rare in broad parameter scans (at most ${\sim}1\%$) and requires high spin ($a/M\gtrsim 0.89$), highly relativistic exhaust ($v_e\gtrsim 0.91c$), and finely tuned initial conditions. Under optimal tuning the success rate reaches ${\sim}70\%$ at $a/M = 0.95$. For representative escape trajectories, a single periapsis impulse is more propellant-efficient than the continuous-thrust controllers studied here. All quoted thresholds are empirical and specific to the orbit family, prior, and steering protocol studied.