The Helical Vacuum Current: Einstein Tensor, Stress-Energy Source, and CSG Framework Connection for the Helical Temporal Metric
Year: 2026
Type: article
Abstract: What sources the helical twist in spacetime? The Helical-Resonant Time Model proposes that temporal structure has a helical geometry encoded in a modified spacetime metric with an off-diagonal coupling between coordinate time and helical phase. Previous papers in this series computed the metric's Christoffel symbols and geodesic equations. This paper closes the final gap in the General Relativity treatment by computing what would have to exist to source that geometry under Einstein's field equations. The Einstein tensor was computed mechanically from the verified Christoffel symbols using SymPy symbolic mathematics. The result was not designed or anticipated: the vacuum stress-energy tensor required to sustain the helical geometry has exactly zero energy density — the time-time component G_tt vanishes through complete algebraic cancellation — combined with anisotropic negative spatial pressure with a precise 2:1 ratio between the pitch axis and transverse directions. We term this source the helical vacuum current. It is not a cosmological constant, not cosmic string tension, and not any standard matter distribution. It is a spatially directed negative pressure with zero net energy density — the signature of a steady-state flow rather than accumulated energy. The 2:1 anisotropy encodes the preferred direction of the helical pitch axis directly in the stress-energy tensor. The zero energy density result connects naturally to the Continuous Spacetime Generation framework: a balanced injection-return cycle would maintain geometric structure through steady-state flow without net energy accumulation, producing exactly this tensor structure. The quantitative bridge is established: CSG injection rate Φ ~ H₀² determines coupling constant α ~ H₀/ω which determines helical vacuum current T_μν^vac ~ H₀²/(8πGc²). The entire hierarchy traces to a single cosmological observable. Energy conditions are analyzed: the weak energy condition is marginally satisfied, the null and strong energy conditions are violated — consistent with dark energy-like sources. The helical vacuum current is approximately 10⁷⁶ times smaller than the observed cosmological constant, explaining why it has not been previously detected. Complete SymPy computation code is provided in an appendix. All results are reproducible in approximately five seconds on standard hardware. This paper completes the four-part series: CSG thermodynamics → helical temporal geometry → geodesic structure → Einstein tensor sourcing. The next step — deriving a minimal action principle that generates the helical vacuum current as its Noether current — is identified as the highest-priority theoretical development.
Author: Bemiss, Michael
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7166322641
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