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 is no physical “surface” as such. The boundaries are more accurately mathematical surfaces, or sets of points in space-time, relevant to analysis of the black hole’s properties and interactions.[1]



  • 1Types of black holes
  • 2Formation
    • 2.1Relation with gamma ray bursts
  • 3Conversion to a Schwarzschild black hole
  • 4Kerr metric, Kerr–Newman metric
  • 5See also
  • 6References

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 an infalling observer falls into a rotating black hole in a finite proper time and with a very high rapidity (left), from the perspective of a coordinate observer at infinity he slows down freezing at the horizon approaching zero velocity relative to a stationary probe on site while being whirled around the horizon with the black hole’s frame-dragging-rate infinitely often (right).

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:

Non-rotating (J = 0) Rotating (J > 0)
Uncharged (Q = 0) Schwarzschild Kerr
Charged (Q ≠ 0) Reissner–Nordström Kerr–Newman


Rotating black holes are formed in the gravitational collapse of a massive spinning star or from the collapse of a collection of stars or gas with a total non-zero angular momentum. As most stars rotate 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 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.

Relation with gamma ray bursts

The formation of a rotating black hole by a collapsar is thought to be observed as the emission of gamma ray bursts.

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

For more details on this topic, see Kerr metric.
For more details on this topic, see 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.

Source: Wikipedia and

By Trinh Manh Do

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