VORTEX Simulator

🌀 VORTEX Simulator

VORTEX ETERNITY | v0.6.7 (Gold Master) | April 15, 2026
Location: viz/vortex_eternity/

"Where equations meet eternity — every orbit, every merger, every collapse, rendered in real time."

What is VORTEX?
VORTEX and GRANITE — Architecture
Physics Engine — Complete Reference
Zero-Allocation Architecture
Rendering Pipeline
Simulation Scenarios
Live Telemetry Dashboard
Camera System
Controls & Keyboard Reference
Cinematic & Recording Tools
Data I/O
Version History
Roadmap: VORTEX v1.0
Physics References

1. What is VORTEX?

VORTEX (VORTEX ETERNITY) is a standalone, browser-native N-body simulation and visualization engine for gravitational astrophysics. It runs entirely inside a single HTML file with no installation, no server, and no external dependencies beyond the bundled Three.js library.

VORTEX is not a toy simulation. It is a research-grade Post-Newtonian engine implementing the full EIH hierarchy through 2PN, with analytical 2.5PN radiation reaction, 1.5PN Lense-Thirring spin-orbit coupling, 2PN spin-spin, and 2PN quadrupole-monopole corrections — all running in a Hermite 4th-order predictor-corrector integrator stabilized by Kahan compensated summation.

What it simulates

Gravitational N-body dynamics under full Post-Newtonian gravity (1PN + 2PN + 2.5PN)
Black hole and neutron star inspiral with gravitational wave energy loss
Lense-Thirring frame dragging and spin precession (exact Rodrigues rotation)
Tidal Disruption Events (TDE) via Roche limit physics
Supernovae and Hypernovae with blast dynamics
Accretion disk formation around compact objects
Kozai-Lidov oscillations, EMRI, galactic center dynamics
Merger mass defect (ΔM_rad), GW recoil kicks
Solar System dynamics, circumbinary planets, pulsar environments

What it renders

Real-time WebGL 3D scene at 60 FPS
Gravitational lensing via custom GLSL Schwarzschild ray-deflection shader
Einstein Cross (4-image lensing) for extreme compact objects
Relativistic Doppler shift (redshift/blueshift) and Lorentz beaming
Body trails, glow halos, accretion disk particles
Live orbital trajectory prediction (ellipse/hyperbola/parabola)
Minimap with Isobar (gravitational potential) and Flux (radiation) sensor modes

2. VORTEX and GRANITE — Architecture

CURRENT STATE (v0.6.7)
─────────────────────────────────────────────────────────────
GRANITE (C++ HPC)              VORTEX (Browser Engine)
  CCZ4 spacetime evolution  →    Standalone PN sandbox
  GRMHD Valencia            →    Independent N-body sim
  HDF5 checkpoints          →    No GRANITE connection yet
  AMR grid hierarchy        →    Own physics integrator

TARGET STATE (v1.0)
─────────────────────────────────────────────────────────────
GRANITE (C++ HPC)              VORTEX (3D Dashboard)
  Full CCZ4 + GRMHD sim     →    Read GRANITE HDF5 files
  Produces HDF5 + JSON      →    Replay spacetime data
  Python distills outputs   →    Render horizon topology
  Kinematic streams         →    Visualize Psi4 GW strain
  Telemetry JSON            →    Interactive NR explorer

VORTEX is the visualization and outreach layer of GRANITE. The C++ backend handles the full non-linear CCZ4 field equations at supercomputer scale. VORTEX handles human perception — making those results tangible, interactive, and beautiful in a browser tab.

The v1.0 integration pipeline:

GRANITE HDF5 checkpoints
        ↓
Python granite_analysis (distillation)
        ↓
JSON kinematic + telemetry streams
        ↓
VORTEX ingest + 3D playback
        ↓
Interactive exploration of NR data

3. Physics Engine — Complete Reference

3.1 Hermite 4th-Order Predictor-Corrector

Reference: Makino & Aarseth (1992), PASJ 44, 141–151

The Hermite scheme evolves both position x and velocity v simultaneously, requiring both the acceleration a and its time derivative — the jerk j = da/dt — at each step. This 4th-order accuracy with jerk is far superior to RK4 for gravitational N-body problems.

Predict step:

x_p = x + v·dt + (1/2)a·dt² + (1/6)j·dt³
v_p = v + a·dt + (1/2)j·dt²

Evaluate: Compute forces and jerks (a_new, j_new) at predicted positions.

Correct step:

v = v₀ + (1/2)(a₀+a₁)dt + (1/12)(j₀-j₁)dt²
x = x₀ + (1/2)(v₀+v₁)dt + (1/12)(a₀-a₁)dt²

Adaptive timestep (Aarseth criterion):

dt = η × sqrt(|a| / |j|)

η is a safety factor. Small steps near close encounters; large steps in the far field — critical for accurate inspiral simulations.

NaN Shield: After every corrector step, all position/velocity components are validated. If NaN or Infinity is detected, the timestep is bisected and retried. After MAX_BISECT = 6 halvings without recovery, the corrupted body is surgically removed and the simulation continues.

3.2 Kahan Compensated Summation

All energy accumulation uses the Kahan compensated summation algorithm to prevent floating-point round-off from accumulating over millions of integration steps:

class KahanSum {
    add(value) {
        const y = value - this.c;    // compensated value
        const t = this.sum + y;      // sum + compensated value
        this.c = (t - this.sum) - y; // capture lost bits
        this.sum = t;
    }
}

The ΔE/E₀ readout in the top bar is the Kahan-tracked symplectic energy error. Values below 0.01% indicate excellent Hamiltonian conservation.

3.3 Post-Newtonian Hierarchy

All PN corrections are togglable at runtime and applied as acceleration + jerk terms in the O(N²) force loop.

1PN — Einstein-Infeld-Hoffmann (Conservative)

Reference: Will (2014), LRRGR §9

a₁^{1PN} = (Gm₂/r²c²) · [n̂·Φ₁ + (4n̂˙₁ - 3n̂˙₂)·v_rel]

Φ₁ = -v₁² - 2v₂² + 4(v₁·v₂) + (3/2)ṅ₂² + 5Gm₁/r + 4Gm₂/r

VORTEX implements the full analytical 1PN jerk (da^{1PN}/dt via chain rule) — not a finite-difference approximation. This is required for Hermite-4 correctness and is rare even in research codes.

2PN — Second Post-Newtonian Conservative (EIH)

Reference: Will (2014) §9.1; Blanchet & Iyer (2003), PRD 71, 024004

O(v/c)⁴ corrections. Active for all body types.

a^{2PN} = (Gm/r²c⁴) · (A₂·n̂ + B₂·v_rel)

A₂ includes: velocity⁴ terms + (Gm/r)·velocity² cross terms + (G²m²/r²) terms
B₂ includes: (n̂·v_b)·velocity² + (Gm/r)·radial projections

2.5PN — Radiation Reaction (Dissipative)

Reference: Blanchet (2014), LRRGR §5

The term that drives inspiral — removes orbital energy at the Peters quadrupole rate:

a^{2.5PN} = (4/5)·G²m₁m₂/(c⁵r³) · [n̂·A_rad + v_rel·B_rad]

A_rad = ṅ·(-6v² + 52GM/3r + 3ṅ²)
B_rad = 2v² - 8GM/r - 3ṅ²

Active only for compact objects: BH and NS types. VORTEX also implements the full analytical 2.5PN jerk (not finite difference).

3.4 Spin Physics

1.5PN Lense-Thirring Spin-Orbit

Reference: Barker & O'Connell (1975); Damour (2001) §4

Full Barker-O'Connell spin-orbit force:

F_SO = (Gμ/r³c²) · {6(n̂×v)(S_eff·n̂) - 3(S_eff·n̂)nv·n̂ + 3nv(S_eff×n̂) - S_eff×v}

S_eff = S₁/m₁ + S₂/m₂  (mass-reduced effective spin)

Spin precession via exact Rodrigues rotation — preserves |S| exactly. Euler integration inflates spin magnitude and is NOT used.

2PN Spin-Spin Coupling

Reference: Barker & O'Connell (1975); Kidder (1995), PRD 52, 821

F₁_SS = (G/m₁m₂c²r⁴) · {15(n̂·S₁)(n̂·S₂)n̂ - 3(S₁·S₂)n̂ - 3(n̂·S₁)S₂ - 3(n̂·S₂)S₁}
F₂_SS = -F₁_SS  (Newton's 3rd — exact for Hamiltonian systems)

2PN Quadrupole-Monopole

Reference: Poisson (1998), PRD 57, 5287

C_Q coefficients:  BH → 1.0   (Kerr metric)
                   NS → 4.0   (canonical stiff EOS)

F_QM = (Gm_b·C_Q)/(2c²m_a²r⁴) · {6(n̂·S_a)S_a + (3S_a² - 15(n̂·S_a)²)n̂}

3.5 Astrophysical Events

Tidal Disruption Events (TDE)

d_Roche = 2.44 · r_phys · (M_massive / M_small)^(1/3)
r_phys = 0.7 · m^(1/3)  [calibrated: 1 M☉ → 0.7 sim-units]

Trigger: r < d_Roche  AND  M_massive ≥ 100  AND  M_small ≥ 0.5

Supernovae / Hypernovae

Hypernova threshold: M_star > 40 M☉ → E_HN = 100 × E_SN

Lethal zone: E_deposited > E_binding → companion evaporates
E_binding = 3GM²/(5R)  (uniform sphere)
Blast: a = E_total·σ / (4πR²·m_companion)

Accretion Disk

ISCO-bounded particle dynamics. Keplerian orbits between visual radius and Kerr ISCO:

r_ISCO = GM/c² · (3 + Z₂ - sqrt[(3-Z₁)(3+Z₁+2Z₂)])
Disk luminosity: L = G·M·ṁ / (2·r_ISCO)

4. Zero-Allocation Architecture

The VORTEX physics hot loop allocates exactly zero objects per frame. This is the architectural foundation that enables 60 FPS under intense computation.

JavaScript's garbage collector pauses execution when it reclaims memory. Naive vector code creates thousands of new THREE.Vector3() per frame → GC stall every few seconds → dropped frames.

Solution: All temporary vectors are pre-allocated at startup:

const _r    = new THREE.Vector3();  // separation vector r₁₂
const _v    = new THREE.Vector3();  // velocity difference v₁-v₂
const _a    = new THREE.Vector3();  // Newtonian acceleration kernel
const _k    = new THREE.Vector3();  // jerk kernel
const _nHat = new THREE.Vector3();  // unit vector n̂ = r̂₁₂
const _pnA  = new THREE.Vector3();  // PN acceleration accumulator
const _pnJ  = new THREE.Vector3();  // PN jerk accumulator

All operations mutate these vectors in-place:

// CORRECT (zero-alloc):
_r.subVectors(b2.position, b1.position);

// WRONG (allocates on heap):
const r = b2.position.clone().sub(b1.position); // NEVER in hot loop

Result at 20 substeps/frame:

Without ZAA: ~40,000 Vector3 allocations/frame → GC every 2 seconds
With ZAA: 0 allocations/frame → GC never triggered by physics

5. Rendering Pipeline

VORTEX uses Three.js r128 as the WebGL abstraction layer.

Body Rendering — InstancedMesh

All N bodies rendered as a single draw call:

Pre-allocate InstancedMesh with MAX_BODIES = 64
Each frame: mutate instanceMatrix[] and instanceColor[] in-place
Single draw call regardless of body count
frustumCulled = false: bodies never clipped at large orbital radii

Gravitational Lensing Shader (GLSL)

Custom ShaderPass post-processing simulates Schwarzschild optical curvature — bending UV coordinates toward each compact object via 1/r² deflection.

Einstein Cross extension: When lensStr > 0.18 (strong-field threshold), 4 additional image samples composited at ±x/±y offsets at Einstein ring radius, Gaussian-weighted:

float w = exp(-8.0 * pow(dist - eRuv*0.55, 2.0));
color += texture(tDiffuse, crossUV) * w * crossStrength;

Relativistic Doppler & Beaming (CPU-Side)

Applied per-body in syncInstances(), mutating iColorData Float32Array in-place:

const beta = dot(v_body, r̂_camera) / C_SIM;
R_channel *= (1 + beta * 1.4);  // receding → redder
B_channel *= (1 - beta * 1.4);  // approaching → bluer
G_channel *= clamp(1 + |beta| * 2.5, 0.25, 3.5);  // Lorentz beaming

Orbital Trajectory Prediction

For selected body: compute Kepler elements analytically from (r, v), trace in orbital plane, transform to world coordinates. Color: green = ellipse, yellow = parabola, red = hyperbola.

6. Simulation Scenarios

Pre-Built Physics Scenarios

Scenario	Bodies	Key Physics	Description
Genesis · 8-Body	8	2.5PN, SO	Default sandbox — diverse BHs, NSs, stars
GW150914 Inspiral	2	2.5PN	Historical LIGO detection configuration
GW170817 Inspiral	2	2.5PN, NS	Binary neutron star (LIGO/Virgo 2017)
EMRI (LISA)	2	2.5PN, SO	Extreme mass ratio inspiral
ZKL Triple	3	Kozai-Lidov	Kozai-Lidov driven merger triple
SgrA Galactic Center*	N	1PN, SO	S-star orbits around Sgr A*
Kozai-Lidov	3	Secular	Inner binary + inclined perturber
TDE Encounter	2	Roche, TDE	Star disruption by SMBH
Retrograde Chaos	N	N-body	Retrograde orbit chaos
Oort Cloud Infall	N	Keplerian	Long-period comet infall
Interstellar Pass-by	2	Hyperbolic	Hyperbolic stellar fly-by
☀ Solar System	9	1PN	Sun + 8 planets
◈ Pulsar Playground	5	2.5PN, SO	Ultra-massive magnetar + planetary system
⊕ Circumbinary Haven	N	Resonance	Tatooine-style circumbinary planet
★ Solar Proxy	N	Keplerian	Sun-like star with Earth-like companion

Observation Missions (Cinematic)

Mission	Description
Total Eclipse	3-body eclipse: star, gas giant, moon in syzygy
Binary Dance	Two neutron stars at extreme proximity
Grand Alignment	5 bodies in grand alignment

Body Classification

Auto-classification from compactness C = G·M / (c²·R):

Type	Compactness C	Notes
BH (Black Hole)	C ≥ 0.25	2.5PN + SO active
NS (Neutron Star)	0.1 ≤ C < 0.25	2.5PN + SO active, C_Q=4.0
DWARF	C < 0.1, M ≥ 1 M☉	Newtonian + 1PN
STAR	M ≥ 100 M☉	Supernova eligible

7. Live Telemetry Dashboard

NR Diagnostics Matrix

Quantity	Symbol	Physical Meaning
α_min Geometric Lapse	α = √(1-2Φ/c²)	Spacetime curvature proxy
Symplectic Energy Error	\|ΔE/E₀\|	Kahan Hamiltonian conservation
L_GW Peters Quadrupole	L_GW [c⁵/G]	Instantaneous GW luminosity
PN Parameter	x = max(v²,GM/r)/c²	Post-Newtonian expansion
Δφ GR Phase Dephasing	Δφ [rad]	GR phase vs Newtonian
M_rad GW Mass Defect	ΔM [M☉]	Total mass radiated as GW
\|S_total\| Lense-Thirring	χ_eff	Effective spin parameter
h₊ / h× GW Strain	h [G/c⁴]	Quadrupole GW strain
M_chirp / T_merge	M_c [M☉]	Chirp mass + merger estimate
f_GW Frequency	f_GW [Hz]	Dominant GW emission frequency
QNM Ringdown	f_QNM	Post-merger quasi-normal mode

Relativistic Diagnostics Window (Chart.js)

Three real-time charts:

e vs a (Orbital Evolution): Eccentricity vs. semi-major axis — traces the Peters inspiral track from initial orbit through circularization to plunge.
f_GW Chirp: GW frequency vs. time on semi-log Y axis. The upward sweep confirms 2.5PN radiation reaction is active.
β² = (v/c)²: Peak relativistic velocity parameter per step. Values β²→0.1 indicate strong-field regime where PN approximation approaches its limits.

MTF time-filter: LIVE / 1YR / 10YR / MAX for historical data replay.

8. Camera System

Mode	Description	Best For
Free Orbit	OrbitControls — drag to rotate, scroll to zoom	General exploration
Track CoM	Follows center of mass	Binary inspiral
Top Down	Fixed overhead view	Orbital plane
Cinematic	Auto-panning slow sweep	Screenshots
🎬 Autopilot	AI director cycling between targets	Long recordings
Surface View	First-person on body surface	Planetary scale

Cinematic Autopilot: Cycles through BH/NS/massive body targets at 12–15s (randomized to prevent periodicity). Camera smoothly lerps to target with factor = 0.04 per frame.

9. Controls & Keyboard Reference

Physics Toggles

Toggle	Effect	Default
1PN	EIH conservative	ON
2.5PN	Radiation reaction / inspiral	ON
L-T SO	Lense-Thirring spin-orbit	ON
Lens	Gravitational lensing shader	ON
Roche	TDE via Roche limit	ON
★ AutoSN	Auto-supernova at end-of-life	OFF
🌊 Shell	Volumetric shockwave shell	ON

Temporal Flow Controls

Speed	Meaning
−100×	Reverse fast
−10×	Reverse slow
0.1×	Ultra-slow
1×	Real-time
10×	Default
100×	Fast forward
500×	Extreme fast
↩ Rewind	Flip time direction

Chronos Rewind: Flips sign of all velocity vectors — time runs backward.

Keyboard Shortcuts

Key	Action
`Space`	Pause / Resume
`R`	Reset scenario
`Z`	Zen Mode (UI hide)
`F`	WASD free-flight toggle
`X`	Supernova on selected body
`[`	Sim-OS Master Menu
`Esc`	Cancel placement / close overlay
`?`	Keyboard reference modal
`Click body`	Select body
`Drag canvas`	Spawn body (slingshot)

10. Cinematic & Recording Tools

Zen Mode

Press Z — all UI fades to invisible (500ms CSS transitions). Only WebGL canvas, vignette, and atmospheric haze remain. Toast notification auto-fades after 3 seconds.

Use case: Screen recording, outreach videos, public demonstrations.

GW Audio Sonification

Real-time chirp synthesizer using Web Audio API:

Frequency: f_audio = clamp(f_GW × 10, 30 Hz, 1200 Hz)
           30 Hz floor → deep inspiral rumble
           1200 Hz ceiling → merger squeal

Amplitude: gain = clamp(|h₊| × 5×10⁶, 0, 0.5)

Signal path: Oscillator → Physics Gain → Master Gain → Output

All parameter updates use AudioParam.setTargetAtTime(τ=0.08s) — zero-alloc, no GC, no click/pop artifacts.

Volume panel: 🔊 button in top bar. Dynamic icon: 🔇 0% / 🔈 40% / 🔉 75% / 🔊 100%.

Cinematic Autopilot Camera

AI camera director. Priority: BH/NS → massive bodies (M>10) → all bodies. Hold 12–15s per target (jittered). Slow lerp factor 0.04 for cinematic smoothness.

11. Data I/O

Export State (JSON)

⬆ EXPORT → Downloads complete simulation snapshot: all body states, time, scenario name, toggle states.

Import State (JSON)

⬇ IMPORT → Restores full simulation from JSON snapshot. Enables sharing and reproducibility.

CSV Export

▤ CSV → Current step telemetry in tabular format: positions, velocities, masses, energy, angular momentum.

Minimap 3.0 — Sensor Modes

Mode	Visualization
Bodies	Body dots + velocity arrows + ISCO reticles
〈〉 Isobar	Gravitational potential Φ = -ΣGM/r with marching-squares iso-contours (8 levels)
🌡 Flux	Bolometric radiation flux F = ΣL/(4πr²) with thermal color ramp

Isobar mode is a scientific-grade visualization of gravitational influence zones not available in any other quick visualizer.

Additional minimap features: camera frustum cone overlay, ISCO proximity pulsing reticles, click-to-select, hover tooltips (name / mass / velocity / gravitational redshift / type), logarithmic radial projection toggle.

12. Version History

v0.6.7 — Gold Master (April 15, 2026)

Zen Mode: Full UI fade (500ms CSS), Z key, toast notification, all UI elements suppressed including #kh shortcut bar.

GW Audio Sonification: Dual gain chain (physics-driven + user volume), zero-alloc via setTargetAtTime, lazy init on first user click (autoplay policy compliant). Frequency: 30–1200 Hz mapped from f_GW.

Cinematic Autopilot: AI camera director with 12–15s jittered hold times, smooth lerp, Event Log feedback on each target switch.

ESC Abort: Universal cancel for all drag/placement operations. Clears slingshot preview from 3D scene.

Master Volume Panel: 🔊 top-bar floating popup with slider, mute toggle, dynamic icon.

FWM Hardening (5 passes): Off-screen initial placement fix; sticky drag on cross-display pointer escape; zoom-aware coordinate transforms; resize boundary violations; HUD-scale-aware window sizing.

v0.6.7 — Sim-OS Audit, Research Visuals & FWM Hardening (April 14, 2026)

NR Diagnostics Window: Three Chart.js panels (e vs a, f_GW chirp, β²). MTF time-filter (LIVE/1YR/10YR/MAX). _clearTelemetry() centralized reset prevents cross-scenario contamination.

Minimap 3.0: Isobar (marching-squares potential), Flux (bolometric), ISCO reticles, click-to-select, hover tooltips, velocity arrows, log-projection toggle, camera frustum, canvas size fix for CSS flex distortion.

Relativistic Doppler & Beaming: CPU-side per-body color modulation, zero-alloc iColorData mutation.

Einstein Cross shader: 4-image secondary lensing at strong-field threshold, Gaussian-weighted.

Master Menu Categorization: 4 sections — Relativistic Optics, Scientific Analysis, Tactical Tools, System.

Phase label overflow fix: max-width: 28vw; text-overflow: ellipsis prevents overwrite of right-side telemetry at high HUD scale.

v0.6.6 — VORTEX WebGL Sim Integration (April 12, 2026)

Initial VORTEX release into the GRANITE ecosystem:

Zero-Allocation Architecture (ZAA)
Hermite 4th-order P-C integrator (Makino & Aarseth 1992)
Kahan compensated summation
1PN + 2PN + 2.5PN full hierarchy with analytical jerks
1.5PN Lense-Thirring SO (Barker-O'Connell + Rodrigues exact rotation)
2PN Spin-Spin (Barker-O'Connell, Kidder 1995)
2PN Quadrupole-Monopole (Poisson 1998)
Roche limit TDE detection
Supernova / Hypernova mechanics
Accretion disk (ISCO-bounded Keplerian particles)
GLSL Schwarzschild gravitational lensing shader
14 pre-built scenarios
Mission Control telemetry (KE, PE, H, L, P, v_max)
GW quadrupole extraction (h₊, h×, M_chirp, f_GW, QNM)

13. Roadmap: VORTEX v1.0

Integration Pipeline (Planned)

[1] GRANITE C++ → HDF5 checkpoints

[2] Python granite_analysis distillation:
    positions.json   (body CoM trajectories)
    horizons.json    (apparent horizon radii vs time)
    gw.json          (Ψ₄ decomposition at extraction radii)
    telemetry.json   (||H||₂, α_center, AMR stats vs step)

[3] VORTEX ingests JSON streams:
    3D body trajectory replay
    Animated apparent horizon visualization
    GW strain h₊/h× as audio + visual overlay
    Constraint norm color-coded spacetime
    AMR grid structure animation

Feature Targets

Feature	Status
GRANITE HDF5 reader (Python)	Planned
JSON stream format spec	Planned
VORTEX JSON playback mode	Planned
Apparent horizon mesh renderer	Planned
Ψ₄ waveform overlay	Planned
AMR grid visualization	Planned
Time-scrub playback control	Planned
Multi-resolution comparison view	Planned

Current Limitations

No GRANITE connection: VORTEX is an independent PN sandbox. It does not read GRANITE HDF5 outputs yet.

PN vs CCZ4: VORTEX uses Post-Newtonian approximations valid for v ≪ c. GRANITE solves the full nonlinear Einstein equations. The two agree only in the weakly relativistic regime.

Merger physics: VORTEX merges bodies into a single object. Quasi-normal mode ringdown is estimated from Kerr formulae, not evolved. Accurate ringdown requires full CCZ4 evolution from GRANITE.

Energy conservation: GW energy loss tracked via Peters formula (2.5PN). Total energy radiated requires full Ψ₄ extraction from GRANITE at multiple extraction radii.

14. Physics References

Reference	Used In
Makino & Aarseth (1992), PASJ 44, 141	Hermite 4th-order P-C integrator
Will (2014), LRRGR §9	1PN EIH acceleration + analytical jerk
Blanchet & Iyer (2003), PRD 71, 024004	2PN EIH (conservative)
Blanchet (2014), LRRGR §5	2.5PN radiation reaction + analytical jerk
Barker & O'Connell (1975), PRD 12, 329	Spin-orbit, Spin-spin coupling
Damour (2001) §4	Full Barker-O'Connell SO expression
Kidder (1995), PRD 52, 821	2PN spin-spin
Poisson (1998), PRD 57, 5287	2PN quadrupole-monopole; C_Q coefficients
Peters (1964), Phys. Rev. 136, B1224	GW energy loss (quadrupole formula)
Nitadori & Aarseth (2012), MNRAS 424	Reference practice for 2.5PN jerk
Kahan (1965), Commun. ACM 8, 40	Compensated summation algorithm
Rodrigues (1840)	Exact rotation formula for spin evolution

VORTEX ETERNITY v0.6.7 — April 15, 2026 — LiranOG
Part of the GRANITE numerical relativity ecosystem

Field	Description
FPS	Rendering frame rate (target: 60)
SUB	Physics substeps per render frame
ΔE	Kahan symplectic energy error (%)
T	Simulated time in years
Bodies	Active body count
Mergers	Merger event count

VORTEX Simulator