Warp Drive Time Ship

This paper proposes a novel approach to manipulate the spacetime metric $g_{\mu \nu }$ by employing gauge-transformed optical soliton beams to generate gravitational solitons, enabling a toroidal time machine to achieve apparent superluminal velocities ranging from $2c$ to ${10}^{7}c$ and induce temporal regression (e.g., ？32.8 years). Our findings demonstrate that the Lagrangian of two optical solitons can be transformed into that of a gravitational soliton via a generalized gauge transformation, involving the coupling of electromagnetic and gravitational fields, with dynamics governed by the invariant Einstein-Maxwell Lagrangian. Utilizing eight tangentially emitted optical soliton beams, combined with meticulous physical computations, we analyze the effects of polarization angle $\theta$ , energy density ${\rho }_{EM}$ , and the number of gravitational soliton pairs ($N$ ) on apparent velocity and closed timelike curves (CTCs), while devising safety control strategies (e.g., precision in $\theta$ ). This study explores the feasibility of this scheme from both theoretical and engineering perspectives, addressing the invariance of the gravitational soliton Lagrangian, curvature engine design, jump velocity mechanisms, and optimizations in structure and safety. The results reveal that this method can substantially enhance navigation speeds and enable time travel; however, challenges related to interstellar voyages and temporal paradoxes warrant further investigation. This work lays a theoretical foundation for future superluminal spacecraft and time machine technologies, heralding the vast potential of gravitational soliton research.