theorem

no-hair theorem

No-hair theorem states that black holes are characterized only by their mass, charge, and angular momentum, with no other distinguishing features.
111 related articles · 2 who worked here

Description

In the 1960s, after the discovery of exact solutions of Einstein's equations for rotating black holes, physicists noticed an amazing property: no matter how complex the initial conditions of collapse, the external gravitational field stabilizes to a form determined only by mass, angular momentum, and charge. John Wheeler dubbed this the no-hair theorem—a black hole has no other 'protrusions' of information. A series of mathematical theorems proved by Israel, Carter, and Hawking confirmed this for stationary black holes.

History

The roots of the theorem go back to 1967, when Werner Israel showed that a static, non-rotating, uncharged black hole must be spherically symmetric (the Schwarzschild solution). Then Brandon Carter and Stephen Hawking generalized the proof to include rotation and charge. John Archibald Wheeler, a master of memorable names, coined the term 'a black hole has no hair' in 1971. Subsequently, the theorem became a cornerstone for the holographic principle and discussions of the information paradox.

How it works

Practically, this allows modeling astrophysical black holes with just a few parameters, which is used in estimates from gravitational-wave signals and shadows from the Event Horizon Telescope. However, the strict theorem is proven for stationary spacetimes with an electromagnetic field; inclusion of other fields or quantum effects can generate 'hair'. For example, in scalar-tensor theories of gravity, scalar hair may exist.

In practice

Astrophysicists determine the parameters of real black holes from the motion of surrounding stars and the radiation of accretion disks, confident that they are not missing anything.

Fun fact

The theorem gave rise to a joke: if a black hole had hair, it could violate the laws of physics by allowing one to guess what fell into it, and thus the information.

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Related articles · 304

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