Definition
The no-hair theorem is the statement that, in classical general relativity, a stationary black hole is completely characterized by three externally measurable parameters: its mass (M), its electric charge (Q), and its angular momentum (J).
Whatever else fell in — chemical composition, magnetic structure, baryon number, the colour of the infalling text — leaves no trace on the exterior geometry. John Wheeler popularized the slogan "black holes have no hair" in the early 1970s.
Why it matters
How it works
The result emerged as a sequence of uniqueness theorems in the 1960s and 1970s. Werner Israel showed that any static, asymptotically flat, vacuum black hole is the Schwarzschild solution. Brandon Carter and David Robinson extended this to the rotating case: any stationary, axisymmetric vacuum black hole is Kerr. Including electric charge gives the Kerr–Newman family. Other classical fields — scalar, fermionic — admit similar no-hair results under reasonable assumptions.
Intuitively, anything that falls into a black hole carries information about its multipole structure (electric, magnetic, gravitational quadrupole, …). Those higher multipoles either fall through the horizon or are radiated away as gravitational waves during the ringdown phase. Once the hole settles into a stationary state, only the conserved quantities — total mass, total charge, total angular momentum, each protected by a Gauss-law-like statement — remain accessible to outside observers.
There are caveats. Magnetic monopoles, in principle, add a fourth charge. Some extensions of general relativity (with scalar fields, higher derivatives, or modified gravity) admit "hairy" black holes. And quantum effects — Hawking radiation, the information paradox — strain the classical statement: if information is to be preserved on evaporation, the hole must, in some quantum-mechanical sense, carry more than three numbers' worth of memory.