The most mysterious objects in the Universe.

Let us examine a few remarkable things that the theory of general relativity predicts about rotating black holes!

It is worth referring here that in 1967 Werner Israel presented at King's College in London his "uniqueness theorem" according to which in the absence of angular momentum, gravitational collapse with sufficient mass will lead to a Schwarzschild black hole, irrespective of the shape of the collapsing star. A classical black hole can be described be only three parameters: Mass, Angular Momentum, Charge. A generic feature of rotating black hole solutions is that, for given mass, their horizon radii are always less than their non-rotating counterparts. While the radius, of a non rotating black hole depends only on its mass, the radius of a rotating black hole depends also on its rotational speed. The grey elliptical region is called ergosphere. Inside the ergosphere, the spacetime itself is in relative motion, because the black hole is actually dragging spacetime while it rotates, and therefore an object there cannot stay stationary. Stationary limit is the outer limit of the ergosphere. It has been suggested that ergosphere can be used to extract energy from rotating black holes (Penrose process). A spherical event horizon still exists, although recently it has been suggested that some rotating black holes in more than 4 dimensions have non-spherical event horizons. A ring singularity exists at the centre, as opposed to the point singularity of a non rotating Schwarzschild black hole. The radius of a Kerr black hole is given by the following equation:

A black hole can be de fined as the number of spacetime points inside the horizon. Super luminal speeds are required for these points to send messages outside the horizon as space is being dragged by the black hole. As we know all stars rotate (even slowly), (Sun needs an average of 27 days to rotate once). When the stars collapse, they accelerate their rotation due to conservation of angular momentum. Therefore we would expect, that only rotating black

holes exist in nature. These black holes are described by the Kerr radius given above.

a=2J/M i.e it is proportional to the angular momentum of the black hole J and inversely proportional to its mass M. It is very important to note that the Newton's gravitational constant is not a dimensionless quantity but has dimensions 1/M^2, while the couplings of weak, strong and electromagnetic interactions are dimensionless quantities. This creates problems for the

quantization of gravity. According to some modified theories of gravity, such as Weinberg's asymptotic safety scenario which was proposed in 1979: "A theory is said to be asymptotically safe if the essential coupling parameters approach a fixed point as the momentum scale of their renormalization point goes to in finity". We will denote this momentum scale with k, with k = 1/r. The infrared limit is when k --> 0 , while the UV limit is when k ---> Infinity. Asymptotic safety, deals with the k --->infinite case. This means that on small scales the gravitational coupling, becomes weak and hence it prevents the formation of a black hole. It implies that at some point the dimensionless strength of the gravitational coupling g=G/k^2 would cease growing with the energy and would tend to a finite limit g*.

The Kerr metric is a generalization to a rotating body of the Schwarzschild metric, discovered by Karl Schwarzschild in 1915, which described the geometry of spacetime around an uncharged, spherically-symmetric, and non-rotating body. The corresponding solution for a charged, spherical, non-rotating body, the Reissner–Nordström metric, was discovered soon afterwards (1916–1918). However, the exact solution for an uncharged, rotating black-hole, the Kerr metric, remained unsolved until 1963, when it was discovered by Roy Kerr. The natural extension to a charged, rotating black-hole, the Kerr–Newman metric, was discovered shortly thereafter in 1965.

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