A No-Go Theorem for Topological Bridges with Matter-Vacuum Coupling

TL;DR

This paper proves that matter-vacuum coupling cannot eliminate the need for exotic matter in traversable topological bridges, reinforcing the importance of classical energy conditions.

Contribution

It establishes a rigorous no-go theorem showing that matter-vacuum coupling cannot bypass the NEC violation required for static topological bridges.

Findings

Matter-vacuum coupling cannot avoid NEC violation in static solutions.

Geometric flare-out condition is incompatible with NEC-compliant sources.

Vacuum interaction gradients obstruct the necessary geometry for topological bridges.

Abstract

Traversable topological bridges traditionally require exotic matter, violating the Null Energy Condition (NEC). This essay investigates whether matter-vacuum coupling can circumvent this necessity. Focusing on zero-tidal-force solutions, we establish a rigorous no-go theorem for static configurations, proving that such coupling cannot bypass the requirement for NEC violation. We demonstrate that the geometric flare-out condition is incompatible with NEC-compliant sources, regardless of the coupling $Q$ or equation of state. Crucially, the vacuum fails to shield the throat; instead, interaction gradients mathematically obstruct the required geometry. This result suggests that causality protection is inherent in the field equations, rendering the vacuum's evolution a regulator rather than a facilitator of topological shortcuts, thereby reinforcing the robustness of classical energy conditions.