In astrophysics, the no-hair theorem states that black holes are completely characterized only by three externally observable parameters: mass, electrical charge, and angular momentum. All other information about the matter which formed a black hole or infalling into it, 'disappear' behind the black-hole event horizon and are therefore permanently inaccessible to external observers. Thus the statement "Black holes have no hair", that is, there are no features that distinguish one black hole from another, other than mass, charge, and angular momentum.

For example, if we "construct" two black holes with the same masses, electrical charges, and angular momenta, but will make the first black hole out of ordinary matter, and the second one out of anti-matter, they would be completely indistinguishable — none of the special particle physics pseudo-charges (baryonic, leptonic, etc.) is conserved in the black hole.

The no-hair theorem was originally formulated for black holes within the context of a four-dimensional spacetime, obeying the Einstein_field_equation of general relativity with zero cosmological constant, in the presence of electromagnetic fields (or optionally other fields such as scalar fields, massive vector fields (Proca fields), spinor fields, etc.). Counterexamples in which the theorem fails are known in spacetime dimensions higher than four; when the cosmological constant is nonzero; in the presence of nonabelian Yang-Mills fields, nonabelian Proca fields, some non-minimally coupled scalar fields, or skyrmions; or in some theories of gravity other than Einstein's general relativity. However, these exceptions are often unstable solutions. It has been proposed that "hairy" black holes may be considered to be bound states of hairless black holes and solitons.

It should be noted, however, that not all theoreticians believe that the "no hair" holds completely even in its original context, when quantum theory is taken into account. For example, Penrose argues that at least some of the information "lost" at the event horizon will be recovered during the quantum-mechanical process of black hole evaporation.

In July 2004 Stephen Hawking presented a new theory about black holes which goes against his own long-held belief in the no-hair theorem. Hawking says the problem with the no-hair theorem is that it implies the black hole will emit the same radiation regardless of what goes into the black hole. So if you throw a pure quantum state into a black hole, you will get out a mixed state. This runs counter to the rules of quantum mechanics (specifically, unitarity), and is known as the black hole information paradox.