OTSOW: Positive-energy control of finite-time traversability in phantom-supported wormholes in four-dimensional general relativity

Abstract

The article, “Positive-energy control of finite-time traversability in phantom-supported wormholes in four-dimensional general relativity” investigates whether a traversable wormhole can be controlled for a finite period within standard four-dimensional Einstein gravity when the exotic matter required to support the throat is separated from the ordinary matter used for dynamical control. The model uses two distinct matter sectors. A free massless phantom scalar field provides the violation of the null energy condition needed to sustain the wormhole throat. A separate positive-energy sector acts as the controller and is constrained by the dominant energy condition at the relevant turning slice. Dynamically, this control sector is represented by nonnegative counter-propagating radial null streams. This separation is central to the paper because it allows the exotic support and the ordinary control mechanism to be analyzed independently. The main analytical contribution is an exact local relation connecting the geometry of the throat to the stress-energy carried by the ordinary controller. At the moment when the throat reaches a strict temporal maximum, this relation becomes a compact three-component budget. The available geometric and matter content is divided among the spatial flare of the throat, the negative acceleration of the aperture, and the amount of dominant-energy-condition slack in the controller. This leads to a turning-point inequality, excludes the standard Ellis flare geometry at a genuine finite-time maximum under the stated assumptions, and provides a lower bound on the duration of controlled aperture protocols. The paper then constructs time-symmetric initial data that saturate the radial dominant-energy-condition boundary. These data are evolved numerically in conformal double-null coordinates using a positive-energy controller built from compact characteristic packets. The simulations follow several independent diagnostics, including null and timelike geodesics, trapping horizons, throat contraction, traveler-frame tidal curvature, Einstein-constraint residuals, and large-domain causal behavior. The first numerical loading study varies the strength of the positive controller while keeping the turning geometry and packet shape fixed. The local timelike crossing threshold is found to be nonmonotonic. For moderate loading it forms a shallow plateau near 0.57 times the speed of light, while stronger loading reduces the threshold to about 0.542 times the speed of light. At the same time, the minimum throat radius decreases and the duration of the transient future-trapped region increases. This demonstrates a clear control trade-off: stronger positive-energy loading can make local timelike passage easier, but it also drives deeper contraction and stronger transient trapping. The main new result of the v0.5 study is the discovery of a resolved strong-loading branch beyond the previously studied loading range. At a controller scale of 1.10, and keeping the original throat-crossing event unchanged, three numerical resolutions produce a convergent local timelike threshold of approximately 0.474 times the speed of light. This is about 12.6 percent lower than the best refined threshold from the earlier baseline study. A direct loading bisection also identifies the transition into the sub-half-light-speed regime near a controller scale of 1.078, showing that the improvement is not restricted to a single isolated numerical point. A second new effect is the sensitivity of traversability to the timing of the crossing. For the same strong-loading geometry, shifting the traveler’s throat-crossing event to the time-symmetric turning slice lowers the refined local threshold further, to approximately 0.443 times the speed of light. This represents an improvement of roughly 18.2 percent relative to the earlier best baseline result. The finding shows that the temporal phase of the traveler’s encounter with the evolving throat is an additional control parameter, rather than merely a passive timing choice. The strong-loading branch is checked independently with null propagation and constraint refinement. The selected null generator remains untrapped, while its minimum areal radius remains stable under refinement. The maximum Einstein-equation residuals over the control region decrease approximately at fourth order as the grid is refined, reaching values below one part in a thousand on the finest reported grid. These convergence results strengthen the interpretation of the strong-loading configuration as a numerically resolved branch rather than a coarse-grid artifact. The calculations also investigate the apparent loss of numerical regularity at still larger controller loading. The location of this failure shifts as the numerical grid is refined, while a loading near 1.14 remains problematic on the finest tested grids. Because this boundary moves with resolution, the article does not interpret it as a confirmed physical collapse threshold. Instead, it is treated as an unresolved strong-loading boundary that requires more advanced numerical methods, such as adaptive mesh refinement or characteristic boundary treatment. The large-domain analysis shows that local wormhole crossing and global escape are not equivalent. A traveler can successfully pass through the throat and reach the opposite finite marker but later be recaptured. By contrast, sufficiently relativistic trajectories remain outward on the audited large domain. The finite-time global escape threshold remains close to 0.966 times the speed of light at the chosen observation time. The paper therefore distinguishes three separate notions: local throat passage, avoidance of transient trapping, and persistent large-domain escape. The article does not claim the discovery of an eternally stable wormhole or a technologically realizable transport system. The model remains classical, relies on a phantom field with a wrong-sign kinetic term, assumes spherical symmetry, and does not establish a theorem at conformal null infinity. It also does not yet provide a fully invariant optimization of the controller energy or a proven physical critical point for strong loading. The originality claim is deliberately restricted. The paper does not claim novelty for phantom-supported wormholes, time-dependent wormholes, radiation-driven manipulation, null-dust descriptions, temporary stabilization, or the passage of ordinary matter through a wormhole by themselves. Its proposed original contribution is the combination of an exact throat-control budget, a maximum-aperture simplex, a dominant-energy-condition-saturating construction, a positive-energy controller separated from the exotic support sector, and an audited loading-and-phase response map that produces a refined local timelike threshold below half the speed of light.