Schwarzchild radius, accretion disk

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A p5js sketch :

How it works :

1. Blackhole class :

class Blackhole {
  constructor(x, y, m) {
    this.pos = createVector(x, y);
    this.mass = m;
    this.rs = (2 * G * this.mass) / (c * c);
  }

• Constructor: Takes x, y, and m as parameters to initialize the black hole’s position (pos), mass (mass), and Schwarzschild radius (rs).
• Schwarzschild radius (rs) is calculated based on the mass of the black hole.

  pull(photon) {
    const force = p5.Vector.sub(this.pos, photon.pos);
    const r = force.mag();
    const fg = G * this.mass / (r * r);
    force.setMag(fg);
    photon.vel.add(force);
    photon.vel.setMag(c);

    if (r < this.rs) {
      photon.stop();
    }
  }

}

• pull Method: Takes a photon object as a parameter.
  • Calculates the force (force) acting on the photon.
  • Computes the distance (r) between the black hole and the photon.
  • Calculates gravitational force (fg) using Newton’s law of gravitation.
  • Adjusts the photon’s velocity based on the force.
  • Checks if the photon is inside the event horizon (rs). If true, stops the photon.

  show() {
    ellipseMode(RADIUS);
    fill(0);
    noStroke();
    ellipse(this.pos.x, this.pos.y, this.rs);

    noFill();
    stroke(100, 100);
    strokeWeight(64);
    ellipse(this.pos.x, this.pos.y, this.rs * 3 + 32);

    stroke(65, 49, 0, 100);
    strokeWeight(32);

    ellipse(this.pos.x, this.pos.y, this.rs * 1.5 + 16);
  }  

• show Method: Draws the visual representation of the black hole.
  • Draws three ellipses representing different aspects of the black hole

when calling m87.show() we get :