Explore how extreme gravity warps spacetime. Adjust the black hole's mass, spin and view angle. Observe the accretion disk, light bending, gravitational lensing and how time slows down near the event horizon.
Each check re-derives a number by a different route (numerical minimisation, geodesic integration, quadrature) and compares it with a closed form or textbook value.
Units. G = c = 1 so lengths are in M = GM/c² (1.477 km per solar mass). The Schwarzschild radius is r_s = 2M.
Kerr hole. Horizon r₊ = M(1+√(1−a²)). The innermost stable circular orbit (ISCO, prograde) follows Bardeen, Press & Teukolsky (1972): 6M at a=0, 1M at a→1. The disc inner edge is placed there. Radiative efficiency η = 1 − E_isco: 5.7% (a=0) to 32% (a=0.998).
Light bending. Rays are integrated per pixel in the Schwarzschild metric: d²u/dφ² + u = 3Mu², u = 1/r. Rays with impact parameter below 3√3 M ≈ 5.196 M are captured: that sets the black shadow. The photon sphere is 3M.
Disc. Thin-disc temperature T⁴ = 3GMṀ/(8πσr³)·[1 − √(r_in/r)] (Shakura-Sunyaev, Newtonian stress). Observed brightness scales with g⁴; g = √(1−2M/r) / (γ(1−β·n)) combines gravitational redshift and Doppler beaming, so the approaching side is brighter. Orbital speed uses Ω = 1/(r^{3/2}+a).
Time dilation. A static clock at r ticks at dτ/dt = √(1 − r_s/r), so distant observers see it slowed by 1/√(1 − r_s/r), which diverges at the horizon.
Orbits. Massive particles obey d²r/dτ² = −M/r² + L²/r³ − 3ML²/r⁴: stable beyond 6M (circles at 3-6M are unstable), the photon orbit is 3M, lower angular momentum plunges. Orbits precess by about 6πM/p per revolution.
Jet. Blandford-Znajek power grows roughly as a²; the visible jet strength follows that scaling and the beaming of the approaching side.
Light bending uses the non-rotating (Schwarzschild) metric; Kerr frame dragging, which shifts and flattens the shadow by up to ~1.5M, is not ray traced. Spin changes the disc edge, horizon, Ω, efficiency, temperature and jet power. The disc is geometrically thin and optically thick with a simple zero-torque temperature profile; colours are a blackbody-like ramp. Orbits in the small panel are Schwarzschild. The lensing panel is a schematic point-lens (Einstein radius not to physical scale). Compare Sizes icons use a logarithmic size scale.
Star-field panorama, galaxy field, disc streak texture and the Earth and Sun icons were rendered in Blender (Cycles, GPU). Real-time ray tracing is a WebGL fragment shader in Three.js. Typical values quoted: Eddington luminosity 1.26×10³¹ W per solar mass, G, c, σ, Rsun, Rearth from CODATA/IAU. Educational, not for research.