Inside the Kerr black hole

Now for the really exciting bit. Let us see how we might extend this new finding from the case of a Schwarzschild black hole to that of the much more common rotating or Kerr black hole. For this, we will need to move to a different coordinate system.

In Boyer-Lindquist coordinates [2], there is a spherical inner event horizon for a Kerr black hole [3] (shown as the red sphere in the diagram above); also in the limit of zero rotation, these coordinates, not unsurprisingly, reduce to standard Schwarzschild coordinates. The metric tensors are different but at the surface of this (inner) event horizon, these differences become insignificant. To understand this fully, see the discussion on comparing infinities. It then follows, that in Boyer-Lindquist coordinates, both the Kerr black hole and the Schwarzschild black hole, have equivalent gravitational fields at their respective event horizons, and consequently, identical internal structures as a result of applying the holographic principle [4] - if the field at all points on the surface of an enclosing sphere is identical, the structure inside the sphere must also be identical.

Let us be absolutely clear here: they are identical in (common) Boyer-Lindquist coordinates but not from a viewing platform here on Earth, that is in Schwarzschild coordinates. From here, the spinning black hole will have an event horizon that is an oblate spheroid, and therefore the internal structure will similarly be stretched in the equatorial plane.

This result should not be all that unexpected. A black hole is effectively cut off from the rest of the Universe so it should not 'know' if it is spinning or not. In addition, using the currently accepted theory, a stationary black hole would have to undergo a non-topological transformation whenever it is spun, which would indeed be a very surprising result - with the point singularity at the origin in the Schwarzschild case having to morph into a ring singularity for Kerr spacetime - but this concern does not seem to have influenced the thinking of other researchers, so far. It is also true that for a Kerr black hole, time also slows to a standstill at the event horizon, and so by the same argument presented in the last section, a rotating black hole also has a Born rigid surface without any recourse to the internal structure.


 Roy Kerr

This leads to an unexpected consequence. We find a difference that is externally measurable, in this model from existing models with a central singularity. Ultimately this should lead to experimental evidence to support those wedded to the idea of a central singularity, or as I believe, to discredit this view.

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Transforming a point into a circle cannot be achieved by a continuous smooth transformation as required for a topological transformation. (Back)