# Ring -singularity (Determinant of the Kerr metric)

1. Feb 18, 2009

### RestlessRiver

"Ring"-singularity (Determinant of the Kerr metric)

My problem is as follows:
"Calculate the determinant of the Kerr metric. Locate the plac where it is infinite. (In fact, this gives the "ring"-singularity och the Kerr black hole, which is the only one)

I got the determinant to :

7a2r4sin4θ+7a4r2sin4θ-8a2r2sin4θ-16Ma2r3sin4θ+16M2a2r2sin4θ-2Ma4rsin4θ+2a2r4sin2θ+a4r2sin2θ+r6sin2θ+2Ma4rsin2θ-4M2a2r2sin2θ-2Mr2sin2θ

all devided by r2 + a2 - 2Mr

where
a=angular momentum/M
M=Mass

and I talked to my prefessor and he told me that the answer should be the equation of a ring (x2+y2 = constant) in spherical coordinates, I have all this in Boyer-Lindquist coordinates I believe, and according to wikipedia

{x} = \sqrt {r^2 + a^2} \sin\theta\cos\phi
{y} = \sqrt {r^2 + a^2} \sin\theta\sin\phi
{z} = r \cos\theta

(http://en.wikipedia.org/wiki/Boyer-L...st_coordinates [Broken])

I don't get it to be an eq of a ring (or circle) .. please help =)

Last edited by a moderator: May 4, 2017