What is a Kerr black hole?

The usual idealised "static" black hole is stationary, unaccelerated, at an arbitarily-large distance from the observer, is perfectly spherical, and has a point-singularity at its centre.

When one of these idealised black holes rotates, it gets an extra property. It's no longer spherically symmetrical , the receding and approaching edges have different pulling strengths and spectral shifts, and the central singularity is no longer supposed to be a dimensionless point.

The equatorial bulge in the event horizon can be deduced in several ways.

• ... as a sort of centrifugal forces effect. Since it's possible to model the (distantly-observed) hole as having all its mass existing as an infinitely-thin film at the event horizon itself (i.e. where the mass is "seen" to be), you'd expect this virtual film to have a conventional-looking equatorial bulge, through centrifugal forces.
• ... as a sort of mass-dilation effect. Viewed from the background frame, the "moving film" of matter ought to appear mass-dilated, and therefore ought to have a greater gravitational effect, producing an increase in the extent of the event horizon. Since the background universe sees the bh equator to be moving faster than the region near the bh poles, the equator should appear more mass-dilated, and should have a horizon that extends further.
• ... as a shift effect. This tidy ellipsoidal shape isn't necessarily what people actually see - it's an idealised shape that's designed to illustrate an aspect of the hole's deduced geometry independent of the observer's viewing angle. In fact, the receding and approaching sides of the hole (viewed from the equator) might appear to have different radii, because it's easier for light to reach the observer from the approaching (blueshifted) side than the receding (redshifted) side (these shifts are superimposed on top of the normal Schwarzchild redshift).
  . If we calculate these motion shifts using either the SR shift assumptions f'/f = (flat spacetime propagation shift) × root[1 - v²/c²] or the plain fixed-emitter shift law f'/f = (c-v)/c, and then treat them as "gravitational", then by multiplying the two opposing shifts together and rooting the result, we can get the same averaged dilation factor of f'/f=root(1 - v²/c²) in each case, and by applying the averaged value, we recreate the same sort of equatorially-dilated shape that we got in the other two arguments.

Of course, none of these "film" arguments work for a rotating point, which immediately tells us that the distribution of matter within a rotating black hole is important, and that the usual method of treating the actual extent of a body within the horizon as irrelevant (allowing the use of a point-singularity) no longer works when the hole is rotating (a rotating hole can't be said to contain a point-singularity).
In the case of a rotating hole, the simplest state that we can claim is equivalent to the rotating film of matter for a distant observer is a ring-singularity.

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