What forces does Geon simulate?

Geon exposes 11 force and correction families: Newtonian gravity, gravitomagnetism, Coulomb electrostatics, magnetic Lorentz force, Yukawa interaction, Higgs and axion field coupling, cosmological expansion, first post-Newtonian correction, spin-orbit coupling, and radiation reaction.

What is the Boris integrator used in Geon?

The Boris integrator is a phase-space-volume-preserving method built around half-kicks and a magnetic rotation. Geon combines it with adaptive substepping and separate correction passes to advance particle trajectories under the enabled interactions.

Does Geon require WebGPU?

No. Geon uses WebGPU compute and instanced rendering when available, then switches to CPU physics and Canvas 2D rendering when WebGPU is unavailable or the device is lost. 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 needs a modern browser with ES modules and Canvas support. A WebGPU-capable browser enables the larger GPU backend; otherwise the simulator uses its CPU physics and Canvas 2D fallback.

Does Geon collect any personal data?

Geon's simulation runs in the browser. Quick saves stay in browser local storage and downloaded saves remain user-controlled; the portfolio site may record aggregate page-view metadata separately from simulation state.

Is Geon free and open source?

Yes. Geon's source is available on GitHub under the GNU Affero General Public License v3.0.

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. Separately, overcharged toy black holes shed same-sign leptons in quantized steps and clamp to the nearest allowed Kerr-Newman charge bound as a numerical backstop.

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 for gravity, electromagnetism, scalar fields, and relativistic corrections. Applicable interactions can use a Barnes-Hut tree, while grid fields and correction terms run in dedicated passes. A Boris integrator advances the particle state with adaptive substeps.

Physics

Eleven force and correction families are exposed: 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, spin-orbit coupling, and radiation reaction. The controls enforce dependencies between coupled mechanisms.

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 cover Keplerian motion, relativistic precession, binary inspiral, Hawking evaporation, atomic and nuclear toy systems, bremsstrahlung, magnetic dipoles, pion exchange, Higgs and axion fields, Peccei-Quinn dynamics, and cosmological expansion.

Gravitomagnetism and Frame-Dragging

Gravitomagnetism is the gravitational analogue of the magnetic force. In Geon, rotating or co-moving masses generate a gravitomagnetic contribution that changes nearby trajectories. Enable the Gravitomagnetic control alongside gravity to isolate the toy model's velocity- and spin-dependent effects.

Black Hole Physics

In black hole mode, particles use a Kerr-Newman-inspired effective radius characterized by mass, charge, and spin. Sub-extremal parameters use the usual outer-horizon formula; super-extremal toy inputs are clamped rather than modeled as physical naked singularities. Gravity switches to a Paczynski-Wiita-style pseudo-potential, so the effective potential steepens near the horizon and particles are swallowed once their centers cross it. 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 effective 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. Overcharged toy black holes shed same-sign leptons in quantized steps and clamp to the nearest allowed Kerr-Newman charge bound as a numerical backstop. 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 discharge.

Boris Integrator

Geon uses the Boris algorithm to integrate particle trajectories. It splits non-magnetic force application into half-kicks around a magnetic rotation, preserving phase-space volume for that core update. Adaptive substepping limits the timestep under high acceleration or cyclotron frequency.

Accessibility

Geon provides keyboard shortcuts, light and dark themes, labeled controls, and numerical readouts for conserved quantities and selected particles. The canvas contains continuous motion and optional particle trails; users sensitive to motion can pause, single-step, or choose a lower-particle preset.

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 horizon capture, Hawking radiation, Schwinger discharge, and extremal charge shedding govern black hole evolution in the toy model; 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).