Rotating black hole

A rotating black hole is a black hole that possesses angular momentum. In particular, it rotates about one of its axes of symmetry.

The boundaries of a Kerr black hole relevant to astrophysics. Note that there are no physical "surfaces" as such. The boundaries are mathematical surfaces, or sets of points in space-time, relevant to analysis of the black hole's properties and interactions.^[1]

Types of black holes

There are four known, exact, black hole solutions to the Einstein field equations, which describe gravity in general relativity. Two of those rotate: the Kerr and Kerr–Newman black holes. It is generally believed that every black hole decays rapidly to a stable black hole; and, by the no-hair theorem, that (except for quantum fluctuations) stable black holes can be completely described at any moment in time by these eleven numbers:

• mass-energy M,
• linear momentum P (three components),
• angular momentum J (three components),
• position X (three components),
• electric charge Q.

While from an infalling observer's perspective the plunge into a rotating black hole occurs in a finite proper time and with very high rapidity (left), from the perspective of a coordinate observer at infinity they slow down, approaching zero velocity at the horizon relative to a stationary probe on site while being whirled around forever by the black hole's frame-dragging effect (right).

Prograde bound orbit around a black hole rotating with a spin parameter of a/M=0.9.

These numbers represent the conserved attributes of an object which can be determined from a distance by examining its electromagnetic and gravitational fields. All other variations in the black hole will either escape to infinity or be swallowed up by the black hole. This is because anything happening inside the black hole horizon cannot affect events outside of it.

In terms of these properties, the four types of black holes can be defined as follows:

Formation

Rotating black holes are formed in the gravitational collapse of a massive spinning star or from the collapse or collision of a collection of compact objects, stars, or gas with a total non-zero angular momentum. As most stars rotate and most collisions have non-zero angular momentum, it is expected that most black holes in nature are rotating black holes.

In late 2006, astronomers reported estimates of the spin rates of black holes in The Astrophysical Journal. A black hole in the Milky Way, GRS 1915+105, may rotate 1,150 times per second,^[2] approaching the theoretical upper limit.

Conversion to a Schwarzschild black hole

A rotating black hole can produce large amounts of energy at the expense of its rotational energy. This happens through the Penrose process in the black hole's ergosphere, an area just outside its event horizon. In that case a rotating black hole gradually reduces to a Schwarzschild black hole, the minimum configuration from which no further energy can be extracted, although the Kerr black hole's rotation velocity will never quite reach zero.

Kerr metric, Kerr–Newman metric

A rotating black hole is a solution of Einstein's field equation. There are two known exact solutions, the Kerr metric and the Kerr–Newman metric, which are believed to be representative of all rotating black hole solutions, in the exterior region.

See also

• Kerr black holes as wormholes
• BKL singularity – solution representing interior geometry of black holes formed by gravitational collapse.
• Penrose process
• Ergosphere
• Black hole Spin-flip
• Black hole bomb
• Stellar black holes

References

Further reading

• C. W. Misner, K. S. Thorne, J. A. Wheeler, J. Wheeler, and K. Thorne, Gravitation (Physics Series), 2nd ed. W. H. Freeman, September 1973.
• Melia, Fulvio, The Galactic Supermassive Black Hole, Princeton U Press, 2007
• Macvey, John W., Time Travel, Scarborough House, 1990