Relativistic Propulsion via Curvature Exchange: Geodesic Acceleration by Ultrarelativistic Gravitational Fields

This work analyzes relativistic energy transfer mediated purely by spacetime curvature within standard general relativity. We consider an idealized two-body scattering scenario in which a payload, modeled as a test particle, interacts gravitationally with a massive driver moving inertially at relativistic speed. The payload follows a timelike geodesic throughout and experiences no proper acceleration; any change in its asymptotic energy arises from spacetime curvature and frame dependence. We summarize known weak-field and exact results showing that the gravitational field of a sufficiently fast-moving mass becomes strongly anisotropic in an asymptotically inertial frame, with a reversal of the longitudinal coordinate acceleration for particles initially at rest when the source speed exceeds a critical threshold β > 1/√3. Working entirely within general relativity and without invoking exotic matter, modified dynamics, or violations of energy conditions, we explore the kinematic consequences of this velocity-dependent interaction. Using exact geodesic motion in the driver rest frame together with Lorentz transformation of asymptotic four-velocities, we derive an explicit two-frame map between the scattering angle in the driver frame and the final energy of the payload in the initial payload rest frame. This formulation isolates the kinematic energy exchange from the dynamical details of the interaction. We identify a “hyperdrive” regime in which the payload exits with a speed exceeding that of the driver in the initial payload frame, analogous to relativistic elastic scattering from a moving source. Closed-form threshold conditions and invariant upper bounds on the achievable payload Lorentz factor are derived. Tidal stresses are estimated using curvature invariants, clarifying the physical constraints on such trajectories. The results are theory-internal and kinematic: they state what general relativity permits in principle for geodesic motion and energy exchange in relativistic scattering. No specific device, engineering realization, or near-term experiment is proposed.