by
Kayll Lake
(gr-qc/0302087)
| It is well known that the Kerr solution (the unique stationary black hole solution in general relativity) has a "ring" singularity. The common wisdom is that all you have to do to show this is calculate the "Kretschmann" scalar (Cabcd Cabcd in this case, Cabcd the Weyl tensor). However, this scalar allows a six-fold infinity of directions along which it need not diverge. To show that the ring of Kerr is singular along every direction of approach (just like the Schwarzschild singularity) it is necessary to also consider the scalar Cabcd *Cabcd where *Cabcd is dual to Cabcd. Whereas this scalar allows a five-fold infinity of directions along which it need not diverge, there is no direction along which both scalars remain finite at the ring singularity. |
| Cabcd*Cabcd and CabcdCabcd plotted simultaneously for all Kerr Balck Holes. Cabcd is the Weyl tensor and *Cabcd its dual. There is no direction along which both Cabcd*Cabcd and CabcdCabcd remain finite, but there are directions along which each remain finite. |