This research presents a theoretical and numerical study of a finite-time traversable wormhole within classical four-dimensional General Relativity.
The model separates the matter content into two physically distinct sectors. A free massless phantom scalar field provides the null-energy-condition violation required to support the wormhole throat, while a separate positive-energy matter sector is used to control the dynamical evolution of the geometry. The control matter is constructed so that it satisfies the dominant energy condition at the turning configuration and can be represented dynamically by nonnegative counter-propagating radial null streams.
A central analytical result of the work is a turning-point constraint relating the temporal acceleration of a symmetric wormhole throat to its spatial flare geometry. This result shows that an Ellis-type throat geometry cannot occur at a strict local maximum of a finite-time opening when the non-phantom control sector satisfies the dominant energy condition. An exact family of initial data saturating the corresponding bound is constructed.
The nonlinear spacetime evolution is then studied numerically in conformal double-null coordinates. The calculations include independent monitoring of the Einstein constraint equations, resolution studies, null and timelike geodesic integration, traveler-frame tidal-force calculations, trapping-horizon reconstruction, and large-domain propagation tests.
The simulations demonstrate a finite operational window during which causal signals and timelike test particles can cross the wormhole. The subsequent evolution contains a transient trapped region rather than a permanently static throat. Depending on the traveler velocity, timelike trajectories may either cross this transient region and later escape, avoid it entirely, or be recaptured by the later dynamics.
Large-domain simulations distinguish local throat crossing from genuine escape toward the opposite asymptotic region. Outgoing null trajectories remain regular and propagate to many tens of throat radii while the geometry approaches an asymptotically flat regime. Fast timelike trajectories also reach the distant opposite region, whereas slower trajectories that successfully cross the local throat can later be turned back.
The results therefore do not describe an eternally stable wormhole. Instead, they provide evidence for a finite-time, dynamically controlled traversability window in classical four-dimensional General Relativity, with the exotic matter responsible for throat support separated from the positive-energy matter responsible for dynamical control.
The accompanying archive contains the publication manuscript, machine-readable numerical results, parameter metadata, convergence studies, trapping-horizon data, large-domain diagnostics, a peer-reviewed literature audit, and an executable source-code snapshot intended to reproduce the principal numerical calculations.