What is the Boris integrator used in Geon?

The Boris integrator is a symplectic method that preserves phase-space volume while handling strong magnetic fields without numerical drift. Geon uses it with adaptive substepping to advance particle trajectories under combined gravitational and electromagnetic forces.

Does Geon require WebGPU?

No. Geon uses WebGPU compute shaders for parallel force calculation when available, but falls back to a Canvas 2D CPU renderer on devices without WebGPU support. Force CPU mode with the ?cpu=1 URL parameter.

What is Barnes-Hut tree acceleration?

Barnes-Hut is a spatial partitioning algorithm that groups distant particles into single nodes, reducing N-body force computation from O(N squared) to O(N log N). Geon uses it for gravity, electrostatics, and Yukawa forces.

What are the system requirements for Geon?

Geon runs in any modern browser. For best performance, use a browser with WebGPU support (Chrome 113+, Edge 113+). The simulator falls back to Canvas 2D rendering if WebGPU is unavailable.

Does Geon collect any personal data?

No. Geon runs entirely in your browser with no server-side processing, no cookies, and no analytics tracking. All simulation state stays on your device.

Is Geon free and open source?

Yes. Geon is licensed under AGPL-3.0 and the source code is available on GitHub. It is free to use for educational and personal purposes.

What is gravitomagnetism in Geon?

Gravitomagnetism (also called frame-dragging) is the gravitational analogue of the magnetic Lorentz force. Moving masses generate a gravitomagnetic field that exerts a velocity-dependent force on other masses, analogous to how moving charges create magnetic fields. Geon simulates this using a gravitomagnetic dipole model where co-moving masses attract more strongly than stationary ones.

What is Schwinger discharge in Geon?

Schwinger discharge models vacuum electron-positron pair production near charged black hole horizons. When the electric field exceeds the critical Schwinger threshold, pairs are torn from the vacuum. The same-sign lepton escapes while the opposite-sign partner falls back in, reducing the black hole's charge by one quantized unit per event. This drives charged black holes toward neutrality and enforces cosmic censorship.

What is superradiance in Geon?

Superradiance is the amplification of a bosonic field by a spinning black hole. When the axion field frequency is below the horizon angular velocity, the field extracts rotational energy from the black hole and grows a scalar cloud around it. The black hole spins down as angular momentum transfers to the field. Extraction stops naturally when the spin drops below the threshold, preventing the black hole from losing all its angular momentum.

Geon — Interactive Particle Physics Simulator

What is Geon?

Geon is a real-time N-body simulator that models how particles move under gravity, electromagnetism, and relativistic effects. It computes pairwise forces between all particles using a Barnes-Hut tree for O(N log N) scaling, then advances trajectories with a Boris integrator that preserves phase-space volume under strong magnetic fields.

Physics

Eleven force types are available: Newtonian gravity, gravitomagnetism (frame-dragging), Coulomb electrostatics, the magnetic Lorentz force, Yukawa interaction, Higgs field coupling, axion field coupling, cosmological expansion via Hubble flow, first post-Newtonian corrections from general relativity, spin-orbit coupling, and radiation reaction. Forces can be toggled independently so students can isolate individual effects.

Scalar Fields

Two scalar fields — Higgs and axion — live on a PQS grid with C² interpolation. The Higgs field modulates particle mass through its local vacuum expectation value, while the axion field couples to charge. Both evolve via Störmer-Verlet integration and exert gradient forces on particles.

Presets

Fifteen curated presets demonstrate specific phenomena: Keplerian orbits, electromagnetic confinement, Rutherford scattering, Higgs potential wells, axion halos, Hubble expansion, gravitational wave inspiral, and more. Each preset configures initial conditions and force parameters to illustrate one concept clearly.

Gravitomagnetism and Frame-Dragging

Gravitomagnetism is the gravitational analogue of the magnetic force. In Geon, rotating or co-moving masses generate a gravitomagnetic field that produces velocity-dependent forces on nearby particles, mimicking the frame-dragging effect predicted by general relativity. This can be seen in the Gravitomagnetic preset, where orbiting masses drag the surrounding space and alter nearby trajectories.

Black Hole Physics

In black hole mode, particles become Kerr-Newman black holes characterized by mass, charge, and spin. Hawking radiation causes evaporation at a rate determined by the Kerr-Newman temperature — smaller black holes radiate faster, leading to runaway evaporation. Charged black holes also undergo Schwinger discharge: the intense electric field near the horizon tears electron-positron pairs from the vacuum, with one lepton escaping and the other falling back in. Each event reduces the black hole's charge by one quantized unit, driving it toward neutrality. Spinning black holes with the axion field enabled exhibit superradiance: when the horizon angular velocity exceeds the axion mass, the field extracts rotational energy and grows a scalar cloud around the black hole, spinning it down until the superradiance condition fails. All charges in the simulation are quantized in units of the boson charge, ensuring discrete conservation across emission, decay, and pair production.

Boris Integrator

Geon uses the Boris algorithm to integrate particle trajectories. The Boris integrator preserves phase-space volume under strong magnetic fields, preventing artificial energy drift that plagues simpler methods like Euler integration. It splits the force application into electric half-kicks and a magnetic rotation, ensuring stable cyclotron orbits at any timestep.

Accessibility

Geon supports keyboard navigation for all controls, high-contrast mode via the theme toggle, and ARIA labels on all toolbar buttons and interactive elements. Simulation parameters are adjustable via labeled sliders and toggles. Known hazards: flashing particle trails and continuous motion simulation. Users sensitive to motion or flashing content should use presets with lower particle counts.

See also: Cyano for cellular energy simulations, Shoals for financial dynamics.

Learning Outcomes

After using Geon, students should be able to: explain how gravitational and electromagnetic forces produce qualitatively different orbital dynamics; describe the role of the Barnes-Hut algorithm in reducing force computation from O(N²) to O(N log N); identify how relativistic corrections (1PN, gravitomagnetism) modify Newtonian predictions at high velocities; distinguish between conservative and dissipative forces in phase-space evolution; describe how Hawking radiation and Schwinger discharge govern black hole evaporation and charge neutralization; and explain how superradiance transfers angular momentum from a spinning black hole to a scalar field.

Prerequisites

Familiarity with Newton's laws of motion and basic vector calculus. No prior knowledge of relativity or particle physics is required — the presets are designed to introduce each concept incrementally.

References

J. Barnes and P. Hut, "A hierarchical O(N log N) force-calculation algorithm" (1986). J. P. Boris, "Relativistic plasma simulation — optimization of a hybrid code" (1970). L. Verlet, "Computer experiments on classical fluids" (1967). J. Schwinger, "On gauge invariance and vacuum polarization" (1951).