Relativistic Astrophysics & General Relativity

Kerr Ergosphere

Simulate Roger Penrose's 1969 energy extraction mechanism from a rotating Kerr black hole. Particles entering the ergosphere ($r_+ < r < r_E$) split into negative energy fragments falling into $r_+$ and escaping fragments with $E_{\text{out}} > E_{\text{in}}$.

Spin Parameter a/M 0.95 (Near Extreme)

Energy Efficiency E_out/E_in 120.7 %

Ergosphere Radius r_E 2.00 r_g

Black Hole Parameters

Black Hole Spin a/M 0.95

Visual Overlay

Show Ergosphere Boundary Ellipse

Show Frame-Dragging Swirl Lines

Show Event Horizon & Particle Badges

Controls

Kerr Metric & Penrose Process Equations

Outer Event Horizon: r_+ = M + √(M² - a²)
Ergosphere Boundary: r_E(θ) = M + √(M² - a² cos²θ)
Penrose Energy Conservation: E_in = E_fall + E_escape (where E_fall < 0 ⇒ E_escape > E_in)

Developer Reference

Core Algorithm & Standalone Script

// Kerr black hole ergosphere Penrose energy extraction engine
const canvas = document.getElementById('canvas');
const ctx = canvas.getContext('2d');
// r_E = M + sqrt(M^2 - a^2 * cos(theta)^2)