Black Holes

When spacetime curves so much that nothing escapes

Where Spacetime Breaks

When enough mass is concentrated in a small enough region, spacetime curves so severely that nothing — not even light — can escape. The boundary of no return is the event horizon. Beyond it, all paths lead inward toward the singularity. Black holes are not exotic curiosities; they are the inevitable endpoint of massive stellar evolution, and supermassive ones anchor the cores of most galaxies.

Gravitational Lensing

A black hole warps the fabric of spacetime so severely that light from background stars is bent, magnified, and distorted. Stars directly behind the black hole form a bright Einstein ring. Nearby stars appear doubled, stretched into arcs, or dramatically displaced from their true positions.

BH Position: (0.50, 0.50)Shadow radius: 0.390

Drag the black hole across the starfield. Stars warp around the photon sphere, forming Einstein rings and multiple images. The dark shadow is the photon capture radius — light that enters never escapes.

Try it: Drag the black hole across the starfield and watch stars warp and dance around it. The dark shadow in the center is the photon capture radius — light that enters never escapes. Adjust the mass to see how the shadow and Einstein ring scale.

Event Horizon, Photon Sphere & ISCO

A Schwarzschild black hole has three critical radii: the event horizon at r = 2M (point of no return), the photon sphere at r = 3M (where light orbits in circles), and the ISCO at r = 6M (innermost stable circular orbit for massive particles). Launch photons at different impact parameters to see capture, orbiting, and deflection.

Event Horizon (r = 2M)
Photon Sphere (r = 3M)
ISCO (r = 6M)
b/bcrit = 1.058(Escapes)
1M (captured)5.2M (critical)12M (escape)

Penrose Diagram of a Black Hole

The Penrose diagram of Schwarzschild spacetime reveals the full causal structure. The singularity is a horizontal line at the top — it's not a place in space, but a moment in the future. Once inside the horizon, hitting the singularity is as inevitable as Tuesday following Monday.

Click anywhere on the diagram to place an event and see its causal future
Event horizon
Singularity
Infalling observer
Hovering observer
Regions: I = our exterior, II = black hole interior (future singularity), III = white hole (past singularity), IV = parallel exterior. Null rays travel at 45 degrees in this diagram.

Rotating Black Holes & Frame Dragging

Real black holes rotate. A rotating (Kerr) black hole drags spacetime around with it — an effect called frame dragging. Outside the event horizon lies the ergosphere, a region where no object can remain stationary, as spacetime itself is swept along faster than light.

Outer horizon (r+ = 1.714M)
Inner horizon (r- = 0.286M)
Ergosphere (r_eq = 2.000M)
Frame-dragged particles
a/M = 0.70
0 (Schwarzschild)0.99 (extremal)
r+1.7141M
r-0.2859M
r_ergo(eq)2.0000M

As spin increases, the ergosphere bulges outward at the equator while the two horizons converge. Inside the ergosphere, all objects must co-rotate with the black hole (frame dragging).

Hawking Radiation

Quantum mechanics adds a twist: black holes aren't perfectly black. Near the event horizon, virtual particle-antiparticle pairs are separated — one falls in, the other escapes as Hawking radiation. Over astronomical timescales, the black hole slowly evaporates, posing deep puzzles about information and the nature of spacetime.

0.5 M☉ (hot)10 M☉ (cold)
Current Mass3.000 M☉
Temperature2.06 x 10^-8 K

Virtual particle-antiparticle pairs spontaneously form near the event horizon. Occasionally one particle escapes while its partner falls in, causing the black hole to lose mass and slowly evaporate. Smaller black holes are hotter and radiate faster.

Key Takeaways

  • Event horizon — The surface from which nothing can escape; at r = 2GM/c² for a non-rotating black hole
  • Gravitational lensing — Light bends around black holes, creating Einstein rings and multiple images
  • Frame dragging — Rotating black holes drag spacetime itself, creating the ergosphere
  • Hawking radiation — Quantum effects cause black holes to slowly evaporate