Rotating black hole

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A rotating black hole (Kerr black hole or Kerr-Newman black hole) is a black hole that possesses angular momentum. It is one of four possible types of black holes that could exist in the theory of gravitation called General Relativity. Black holes can be characterized by three (and only three) quantities M, J and Q, namely:

• mass M, (Schwarzschild black hole if J=0 and Q=0)
• angular momentum J (Kerr black hole if J not zero and Q=0)
• electric charge Q (charged black hole or Reissner-Nordstrøm black hole if Q not zero and J=0; or a Kerr-Newman black hole if both J and Q not zero).

	Non-rotating (J = 0)	Rotating ()
Uncharged (Q = 0)	Schwarzschild	Kerr
Charged ()	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 with an average 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 actual spin rates of black holes in Astrophysical Journal. A black hole in the Milky Way, GRS 1915+105, may rotate 1,150 times per second,^[1] approaching the theoretical upper limit.

A rotating black hole can produce large amounts of energy at the expense of its rotational energy. 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. The formation of a rotating black hole by a collapsar is thought to be observed as the emission of gamma ray bursts.

[edit] Ergosphere and the Penrose process

Main article: Penrose process

A black hole in general is surrounded by a spherical surface, the event horizon situated at the Schwarzschild radius, where the escape velocity is equal to the velocity of light. Within this surface, no observer/particle can maintain itself at a constant radius. It is forced to fall inwards, and so this is sometimes called the static limit.

Two important surfaces around a rotating black hole. The inner sphere is the static limit (the event horizon). It is the inner boundary of a region called the ergosphere. The oval-shaped surface, touching the event horizon at the poles, is the outer boundary of the ergosphere. Within the ergosphere a particle is forced (dragging of space and time) to rotate and may gain energy at the cost of the rotational energy of the black hole (Penrose process).

A rotating black hole has the same static limit at the Schwarzschild radius but there is an additional surface outside the Schwarzschild radius named the "ergosurface" given by (r − GM)² = G²M² − J²cos²θ in Boyer-Lindquist coordinates, which can be intuitively characterized as the sphere where "the rotational velocity of the surrounding space" is dragged along with the velocity of light. Within this sphere the dragging is greater than the speed of light. So, within this sphere, no observer/particle can maintain itself in a non-rotating orbit, but is forced to become co-rotated.

The region outside the event horizon but inside the sphere where the rotational velocity is the speed of light, is called the ergosphere (from Greek ergon meaning work). Particles falling within the ergosphere are forced to rotate faster and thereby gain energy. Because they are still outside the event horizon, they may escape the black hole. The net process is that the rotating black hole emits energetic particles at the cost of its own total energy. The possibility of extracting spin energy from a rotating black hole was first proposed by the mathematician Roger Penrose in 1969 and is thus called the Penrose process. Rotating black holes in astrophysics are a potential source of large amounts of energy and are used to explain energetic phenomena, such as gamma ray bursts.

[edit] Two event horizons

A rotating black hole is very different from a Schwarzschild black hole in that the spin of the black hole will cause the creation of two event horizons, an inner one and an outer one. As the spin increases, the inner event horizon moves outward, and the outer one moves inward. If the spin is great enough, the two will eventually merge and shrink towards the singularity. With no event horizons to hide it from the rest of the universe, the black hole ceases to be a black hole and will instead be a naked singularity.^{[citation needed]}

Due to the two event horizons, a rotating black hole is also required to have two photon spheres, an inner and an outer one. The greater the spin of the black hole is, the farther from each other the photon spheres move. A beam of light travelling in a direction opposite to the spin of the black hole will circularly orbit the hole at the outer photon sphere. A beam of light travelling in the same direction as the black hole's spin will circularly orbit at the inner photon sphere.

[edit] Kerr metric, Kerr-Newman metric

A rotating black hole is a solution of Einstein's field equation. This solution, the axis-symmetric metric of spacetime associated with a point mass containing angular momentum and vacuum outside, was obtained by Roy Kerr in 1963 and is called the Kerr metric. In 1965, Ezra Newman found the axis-symmetric solution for Einstein's field equation for a black hole which is both rotating and electrically charged. This solution is called the Kerr-Newman metric . A black hole with charge and spin has the same gyromagnetic ratio as an electron. Its magnetic moment divided by angular momentum is equal to its charge divided by mass.

While the Kerr and Kerr-Newman metrics are valid solutions to Einstein's field equations, the interior region of the solution appears to be unstable, much like a pencil balanced on its point (Penrose 1968). Therefore some care must be taken to distinguish the axis-symmetric interior geometry of the Kerr metric from the interior geometry of a black hole formed by gravitational collapse, which is probably not axis-symmetric.

[edit] Kerr black holes as wormholes

A Penrose diagram for the Kerr metric: an object travelling on worldline B can emerge out of the spinning black hole.

Because of its two event horizons, it might be possible to avoid hitting the singularity of a spinning black hole, if the black hole had a Kerr metric. At the outer event horizon, the properties of spacetime allow objects to move only towards the singularity. However, when an object passes the inner event horizon, the object is able to move in directions away from the singularity, pass through another set of inner and outer event horizons, and emerge out of the black hole into another universe or another part of this universe without traveling faster than the speed of light (following a time-like path). Unfortunately, it is unlikely that interior metric of a black hole is the Kerr metric.^[2] However, it is not currently known whether or not the actual geometry of a rotating black hole would provide a similar escape route for the infalling traveller via the inner horizon.

[edit] See also

• BKL singularity – solution representing interior geometry of black holes formed by gravitational collapse.

Black holes by mass:

• Micro black hole – an extra-dimensional black hole
• Primordial black hole – a black hole left over from the Big Bang
• Stellar black hole – formed by the gravitational collapse of a massive star
• Intermediate-mass black hole – mass between stellar and supermassive
• Supermassive black hole – mass in the range of 10⁵ to 10¹⁰ solar masses

[edit] References

1. ^ http://www.cosmosmagazine.com/node/873
2. ^ arXiv:gr-qc/9902008

• Penrose R (1968). in ed C. de Witt and J. Wheeler: Battelle Rencontres. W. A. Benjamin, New York.