In the no-hair theorem, black holes are described by mass, electric charge, and angular momentum.
The phrase “no hair” means that, after a black hole settles into a stationary state, outside observers cannot identify the details of the matter that formed it. In the idealized framework of four-dimensional general relativity with electromagnetism, the remaining independent properties are mass, electric charge, and angular momentum. Angular momentum is commonly called spin.
The theorem connects several important exact solutions. A non-rotating, uncharged black hole is represented by the Schwarzschild metric; a rotating one by the Kerr metric; and a rotating, charged one by the Kerr–Newman metric. The black hole’s magnetic moment and geometry are determined by these primary parameters rather than being separate “hair.”
The slogan is useful but simplified. The general no-hair statement is more accurately called a conjecture in some contexts, because proofs require restrictive assumptions and counterexamples exist in alternative theories or higher-dimensional settings. Magnetic field, luminosity, and temperature are not the requested third classical parameter.