The J-Tensor and Ball Lightning: Geometric Field Trapping in Vacuum Phase Space

Introduction

This article proposes a new model for understanding ball lightning as a geometric phenomenon arising from field-based vacuum dynamics. Building on a reformulation of Maxwell's equations into an Einstein-like field equation using a J-tensor, the model interprets ball lightning as a temporary curvature bubble in electromagnetic field space. This phenomenon may be stabilized by vacuum phase delay, charge boson dynamics, and feedback coherence across field geometry. I am currently seeking collaborators — physicists, engineers, or mathematicians — who are interested in helping develop this model further through theoretical refinement, simulation, or experimental design.

Part 1: Deriving the Field Equation from Maxwell's Equations

Recap: The J-Tensor as a Source of Vacuum Geometry

In standard electromagnetism, Maxwell's equations describe how electric and magnetic fields evolve and interact with charge and current. In this model, we elevate these dynamics into a geometric framework, introducing the J-tensor \( J_{\mu\nu} \) as a geometric source that plays a role analogous to the energy-momentum tensor in general relativity.

We begin with the inhomogeneous Maxwell equation:

\[ \partial_\mu F^{\mu\nu} = \mu_0 J^\nu \]

We reinterpret \( J^\nu \) as a projection of a more fundamental geometric object: \( J_{\mu\nu} \), which encodes not only current density but also synchronization terms, field phase curvature, and local vacuum delay effects. The field equation becomes:

\[ G_{\mu\nu} = \kappa J_{\mu\nu} \]

Here, \( G_{\mu\nu} \) is a curvature-like term constructed from derivatives of the electromagnetic field tensor and possibly from higher-order terms involving field synchronization.

Ball Lightning as a J-Tensor Singularity

Ball lightning is proposed to be a localized region of intense field curvature — a J-tensor singularity. A lightning strike acts as a trigger, creating a spike in vacuum energy density and disrupting phase coherence in surrounding fields. This forms a temporary 'J-hole' — a bubble where the electromagnetic field geometry becomes sharply curved, trapping energy inside.

Consequences for Stability and Dynamics

Inside the bubble, the J-tensor geometry stabilizes rotating E and B fields, similar to the standing wave pattern of a photon, but in a localized and curved space. The internal dynamics are phase-locked by vacuum delay and charge boson feedback. The ball's erratic motion arises from asymmetries in J-tensor curvature across the environment, pushing it in unpredictable directions.

Collapse and Release

When synchronization between \( G_{\mu\nu} \) and \( J_{\mu\nu} \) breaks down, energy can no longer be coherently recycled. The structure collapses, possibly producing a flash, electromagnetic pulse, or audible "pop" — consistent with observational reports. The decay is akin to the release of stored field curvature energy.

Experimental Predictions

• Rotating EM signature: Localized EM waves may show non-Maxwellian behavior such as angular momentum or anomalous polarization.
• Phase lag in surrounding fields: Detectors could identify delayed field propagation consistent with vacuum memory.
• Non-thermal emission spectrum: Emissions may differ from chemical plasmas, showing signs of internal field coherence.
• Localized charge boson feedback: Interactions with materials might reveal boundary anomalies or induced currents.

Part 2: Ball Lightning and the Black Hole Analogy

Ball lightning can be understood as the electromagnetic analogue of a black hole — a self-sustaining curvature bubble formed by nonlinear behavior of the J-tensor. Like a gravitational black hole, it:

• Traps energy through geometric curvature (in field space, not spacetime).
• Exhibits boundary behavior analogous to an event horizon (a "J-horizon").
• Persists temporarily due to phase-locked feedback and vacuum delay.
• Eventually decays as the internal field coherence breaks down.

Just as a black hole can warp spacetime, a J-hole warps electromagnetic field geometry and traps energy within a vacuum phase space bubble.

Conclusion

This article introduces a new perspective on ball lightning — not as a chaotic plasma, but as a structured geometric object formed through feedback in vacuum field dynamics. If correct, this model could offer testable predictions about electromagnetic curvature, field delay, and charge boson behavior. The idea is still in development, and I welcome further input, refinement, and collaboration.

Related Work

See Part 1 of this work: Ball Lightning as a Vacuum Phase Bubble