The math seems to suggest R=a, or simply the spin in terms of length. It's certainly an oversimplification, as the answer will depend on the choice of metric.
Here's the best resources I've been able to find on the question. Roy Kerr himself responded to the Quora question:
> There is no Newtonian singularity at the Center of the earth and there is no singularity inside a rotating black hole. The ring singularity is imaginary. It only exists in my solution because it contains no actual matter. When a star collapses into a black hole it keeps shrinking until the centrifugal force stabilizes it. The event shell forms between the star and the outside. In 57 years no one has actually proved that a singularity forms inside, and that includes Penrose. instead, he proved that there is a light ray of finite affine length. This follows from the “hairy ball theorem”.
The stack overflow answer seems to describe the problem in terms I can better understand:
> It seems unlikely to me that you're going to be able to formulate a notion of diameter that makes sense here. Putting aside all questions of the metric's misbehavior at the ring singularity, there is the question of what spacelike path you want to integrate along. For the notion of a diameter to make sense, there would have to be some preferred path. Outside the horizon of a Schwarzschild black hole, we have a preferred stationary observer at any given point, and therefore there is a preferred radial direction that is orthogonal to that observer's world-line. But this doesn't work here.
Here's the best resources I've been able to find on the question. Roy Kerr himself responded to the Quora question:
> There is no Newtonian singularity at the Center of the earth and there is no singularity inside a rotating black hole. The ring singularity is imaginary. It only exists in my solution because it contains no actual matter. When a star collapses into a black hole it keeps shrinking until the centrifugal force stabilizes it. The event shell forms between the star and the outside. In 57 years no one has actually proved that a singularity forms inside, and that includes Penrose. instead, he proved that there is a light ray of finite affine length. This follows from the “hairy ball theorem”.
The stack overflow answer seems to describe the problem in terms I can better understand:
> It seems unlikely to me that you're going to be able to formulate a notion of diameter that makes sense here. Putting aside all questions of the metric's misbehavior at the ring singularity, there is the question of what spacelike path you want to integrate along. For the notion of a diameter to make sense, there would have to be some preferred path. Outside the horizon of a Schwarzschild black hole, we have a preferred stationary observer at any given point, and therefore there is a preferred radial direction that is orthogonal to that observer's world-line. But this doesn't work here.
https://physics.stackexchange.com/questions/471419/metric-di...
https://www.quora.com/What-is-the-typical-diameter-roughly-o...