Steering a warp drive without exotic matter

Abstract

A useful warp drive must accelerate, yet every compact positive-energy construction is static or constant-velocity; accelerating ones need exotic matter, abandon the dominant energy condition (DEC), or are non-compact (no Bondi four-momentum to balance). We construct a compact positive-energy object driven by photon-rocket recoil on a tidally shielded flat cavity. Bondi--Sachs balance, read as propulsion: any asymptotically flat, confined dominant-energy drive changes Bondi four-momentum only by radiating to null infinity, so it cannot steer without radiating. A Kinnersley photon-rocket exterior with prescribed passenger worldtube fixes the thin shell, whose flat interior is a warp drive. Bulk energy conditions collapse to $n^2\ge 0$; steering obeys the closed-form law $-\dot{m}\ge 3m|\hat{I}\pm |$, paid by Bondi mass loss, and both budget and kinematic ceiling survive a positive $\hat{I}›$ to all orders. Our result is existence: admissible shells exist at small acceleration about a static anchor (surface DEC for $2m/R<24/25$), and a slow fixed-axis burn assembles into one real-analytic spacetime, its constant-$u$ cuts characteristic (shell fixed order-by-order, not Cauchy-evolved); the rotating axis stays open. The acceleration-compactness frontier is bracketed by rigorous and closed-form bounds. Minimum-radiation steering is the gravitational-wave-silent Damour dipole, a hyperbolic geodesic with Tsiolkovsky constant $3$, universal in the news-silent class: the $3$ is the collimation penalty over a floor of $1$. The radiating equilibrium is linearly unstable (flux anti-damps the radial mode), yet growth $\sim$ luminosity is bounded over finite burns by the fuel budget. The drive is causal, subluminal, a reaction drive needing no exotic matter in the thin-shell idealization: steering a warp drive is a problem of energy budget, not negative energy.

57 pages, 4 figures, 1 table. v3: adds the frontier bracket + closed-form kinematic ceiling, the positive-Λ budget to all orders, distributional ADM positivity, the finite-duration time-evolved worldtube, the radiating-mode instability and O(μ) wall back-reaction, and optimal-control maneuver design

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