Black Hole Simulator

A real-time 3D black hole physics simulator , featuring gravitational lensing, accretion disk dynamics, N-body black hole interactions, and tidal disruption events. You can explore the open-source repository on GitHub.

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Features

Black Holes

• Multiple black holes with independent mass, spin (Kerr parameter a), position and velocity
• N-body gravitational interaction using the Paczyński–Wiita pseudo-Newtonian potential
• Black hole mergers — momentum conserved, ~5% mass-energy radiated as gravitational waves (Christodoulou formula), spin approximated from angular momentum
• Hawking evaporation — mass loss rate ∝ 1/M²
• Kerr event horizon radius: r₊ = GM + √(G²M² − a²)
• Photon sphere, ISCO (prograde Kerr), shadow radius all derived per-BH

Accretion Disk

• Keplerian thin disk with temperature profile T ∝ (r/r_ISCO)^−3/4 (Novikov–Thorne)
• Doppler shift — blueshift approaching side, redshift receding side
• Gravitational redshift — colors fade toward infrared near the horizon
• Lense–Thirring precession (frame dragging) for spinning black holes
• Photon ring reconstructed from disk particle angular distribution

Planet & Body Simulation

• GasPlanet: tidal spaghettification, Roche limit disruption, comet-tail debris stream
• CelestialBody: hard rocky object, gravitational infall, EH fade
• Time dilation for objects near the horizon (Schwarzschild factor)
• Objects accrete into the BH on crossing the event horizon

Particles

• Free particle system with RK4 integration under multi-BH gravity
• PARTICLE_FORCE: optional weak inter-particle gravity (self-gravity, O(N²) branchless)
• PARTICLE_AUTO_ZOOM: perspective-correct particle size (size ∝ 1/depth)
• Thermal glow — velocity-dependent color shift toward blue-white
• Absorbed by BH when crossing rs, released when disk is disabled

Stars & Lensing

• Realistic 3D star sphere (80 000 px radius) — stars fixed in world space, rotate with camera
• Gravitational lensing of stars and particles using thin-lens deflection angle: δφ = 4GM / (rc²)
• Einstein ring formation when source, BH, and observer are aligned

Camera

• Free-fly 3D camera with perspective projection
• Mouse drag rotate, WASD move, Space/Ctrl up/down
• Time dilation on camera — sim slows down as camera approaches horizon

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Controls

Camera

Key	Action
Mouse drag	Rotate
W / A / S / D	Move forward / left / back / right
Space / LCtrl	Move up / down
LShift	Speed ×3
Arrow keys	Rotate camera

Black Holes

Key	Action
H	Spawn BH in front of camera
[ / ]	Cycle selected BH
M / N	Mass ±0.05 M_geo
K / J	Spin ±0.05

Objects

Key	Action
B	Spawn GasPlanet
V	Spawn CelestialBody

Toggles

Key	Action
Tab	Open / close config panel
O	Pause / Resume
Z / X	Time lapse ±0.5×
P	Physics mode: realistic ↔ 2-body
T	Camera time dilation ON/OFF
E	Hawking evaporation ON/OFF
G	BH gravity ON/OFF
F	BH mergers ON/OFF
Y	Virtual accretion disk ON/OFF
C	Free particles visible ON/OFF
R	Redshift fading ON/OFF
I	Particle temperature glow ON/OFF
U	Spaghettification ON/OFF
S	Realistic 3D stars ON/OFF
ESC / Q	Quit

Config Panel (Tab)

Navigate with ↑↓, adjust value with ← →.

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Physics & Algorithms

Spacetime & Gravity

• Kerr metric — event horizon, ISCO, photon sphere computed analytically
• Paczyński–Wiita potential — pseudo-Newtonian approximation for N-body BH interactions: V(r) = −GM / (r − r_s)
• Schwarzschild gravitational redshift: z = 1 / √(1 − r_s/r)
• Geodesic integration — RK4 on the Schwarzschild effective potential for disk particles

Gravitational Lensing

• Thin-lens approximation: θ± = (β ± √(β² + 4θ_E²)) / 2
• Einstein radius: θ_E = √(4GM · D_LS / (c² · D_OS · D_OL))
• Applied to stars, particles, and celestial bodies; produces Einstein rings and double images

Orbital Mechanics

• Keplerian angular velocity: ω = √(GM) · r^−3/2
• Lense–Thirring frame dragging: Δω = 2GM·a / r³
• Novikov–Thorne disk temperature: T ∝ r^−3/4 · (1 − √(r_ISCO/r))^1/4

Mergers

• Christodoulou formula approximation: M_final = (M₁+M₂) · (1 − 0.0523η), η = M₁M₂/(M₁+M₂)²
• Spin from angular momentum: a_final ≈ (L_1 + L_2 + L_orb) / M_final²

Spaghettification

• Roche limit tidal disruption: intensity = 1 − r/r_Roche
• Shrink rate ∝ intensity², debris stream inherits orbital tangential velocity (TDE debris stream model)

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Thank you for using my project! If you enjoy exploring this simulation, please consider leaving a rating or supporting my work.

Connect & Support:

• Follow my development logs on YouTube
• Check out the source code on GitHub
• Connect with me on Facebook

If you encounter any issues or bugs, please leave a comment on this game page. Enjoy the spacetime simulation! ',:)