The no-hair theorem

The argument

Black holes are complicated objects: born at the death of a star, they have immense mass, infinite density, and infinite gravity, and warp the fabric of spacetime into a single dimension. Yet a theorem known as no-hair theorem states that all this complexity is hidden behind the event horizon and that on the outside black holes can be described with just three quantities. All information about the black hole and what has gone into it besides these three aspects is lost behind the event horizon and cannot be interpreted or measured. No-hair theorem describes black holes by three attributes: mass, electric charge, and angular momentum. Mass is the amount of matter compacted in the center of the black hole. Electric charge is the overall electromagnetic charge that the black hole possesses. Angular momentum is which direction, and how forcefully, the black hole is spinning. Every other property the infalling matter once had — what it was made of, how it was arranged, where it came from — leaves no trace that an outside observer can reach. The consequence is a strikingly simple description of an extreme object. Regardless of how they form or what matter they have enveloped, black holes that have the same values for these three numbers are indistinguishable. Two black holes assembled from entirely different histories are, from the outside, the same object, because the event horizon does not transmit the difference between them. That is what makes the no-hair theorem a statement about the properties of a black hole rather than a convenient approximation of them: the three quantities are not a summary of what has been observed so far, they are the whole of what the outside is able to know.

Premises

Counter-arguments

Some black holes do have hair. The no-hair theorem only applies to isolated black holes that are not interacting with matter. When interacting with matter other properties of black holes are visible, and this is the case with most black holes. In addition, black holes do have more complexity within the event horizon. Just because it isn't visible to an outside observer does not mean that it isn't there.

Rejecting the premises

[Rejecting P1] Several of these descriptions are loose. Not all black holes form from stellar collapse — supermassive black holes and hypothesised primordial ones do not — and "infinite density and infinite gravity" describes a singularity at which general relativity stops giving answers rather than a measured property. Spacetime is curved by the mass, not warped into a single dimension. [Rejecting P2] The result is narrower than stated. It is a family of theorems for stationary, isolated, asymptotically flat solutions, and remains a conjecture rather than a proved theorem in the general case; real black holes sit within accretion discs, magnetic fields and companion systems, where further observable structure is present. The premise also treats information as simply lost, which is the open problem in the field rather than a settled consequence. [Rejecting P3] Indistinguishability holds for the exterior solution, not for the object. That an outside observer can measure only three parameters is a statement about what is accessible — and it is precisely why the information paradox is a paradox. The stronger reading, that nothing further exists, is what the counter-argument disputes and what work on horizon microstructure is directed at.