Three Radii of a Black Hole

Plate 33 speaks for itself: “Three circles: no return, light's orbit, last stable orbit.”

The Physics

Around a non-spinning black hole three radii matter: the event horizon at r_s, the photon sphere at 1.5 r_s where light can circle, and the innermost stable circular orbit at 3 r_s.

r_s = 2 G M / c²

• r_s: Schwarzschild radius, m
• G: gravitational constant, m³ kg⁻¹ s⁻²
• M: mass, kg
• c: speed of light, m s⁻¹

For the Sun, r_s ≈ 2.95 km. Schwarzschild, 1916; non-spinning hole.

Sources

• K. Schwarzschild, Sitzungsber. Preuss. Akad. Wiss., 189 (1916).

On the poster

Plate 033, “Three Radii of a Black Hole”: the pixel-art plate with its slogan “Three circles: no return, light's orbit, last stable orbit.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.