Numerical Indications of Trapped Surface Formation via Resonant Vacuum Polarization without Explicit Exotic Matter Sources

Abstract In conventional General Relativity, the formation of traversable wormhole geometries is typically associated with violations of the Null Energy Condition (NEC). In this work, we present numerical results indicating that NEC-violating effective behavior may arise purely from geometric dynamics without prescribing any exotic matter fields. The simulations solve the full, non-linear Einstein equations using the Einstein Toolkit (Cactus framework/BSSN formulation). A controlled, time-dependent geometric modulation inspired by the Riemann Zeta function is introduced. The results reveal the formation of localized Marginally Outer Trapped Surfaces (MOTS) and transient NEC violation, suggesting that resonant geometric excitation alone can drive non-trivial topological features in vacuum. Version 2.0 Update Notes: Regularization: Explicitly defined the logarithmic offset parameter (t+e) to demonstrate regularity at t=0. Nomenclature: Added a detailed table of symbols to clarify the distinction between the chirp rate and the lapse function. Numerical Specs: Included explicit solver specifications (RK4 integrator, Radiative Boundary Conditions) and a Nyquist-Shannon resolution analysis confirming the absence of aliasing artifacts. Parameters: Explicitly listed the truncated Zeta zero modes used in the modulation ansatz.