An explanation of the Newman-Janis Algorithm

After the original discovery of the Kerr metric, Newman and Janis showed that this solution could be ``derived'' by making an elementary complex transformation to the Schwarzschild solution. The same method was then used to obtain a new stationary axisymmetric solution to Einstein's field equations now known as the Kerr-newman metric, representing a rotating massive charged black hole. However no clear reason has ever been given as to why the Newman-Janis algorithm works, many physicist considering it to be an ad hoc procedure or ``fluke'' and not worthy of further investigation. Contrary to this belief this paper shows why the Newman-Janis algorithm is successful in obtaining the Kerr-Newman metric by removing some of the ambiguities present in the original derivation. Finally we show that the only perfect fluid generated by the Newman-Janis algorithm is the (vacuum) Kerr metric and that the only Petrov typed D solution to the Einstein-Maxwell equations is the Kerr-Newman metric.Comment: 14 pages, no figures, submitted to Class. Quantum Gra

The Newman-Janis Algorithm, Rotating Solutions and Einstein-Born-Infeld Black Holes

A new metric is obtained by applying a complex coordinate trans- formation to the static metric of the self-gravitating Born-Infeld monopole. The behaviour of the new metric is typical of a rotating charged source, but this source is not a spherically symmetric Born-Infeld monopole with rotation. We show that the structure of the energy-momentum tensor obtained with this new metric does not correspond to the typical structure of the energy momentum tensor of Einstein-Born-Infeld theory induced by a rotating spherically symmetric source. This also show, that the complex coordinate transformations have the interpretation given by Newman and Janis only in space-time solutions with linear sources

Spinning up asymptotically flat spacetimes

We present a method for constructing stationary, asymptotically flat, rotating solutions of Einstein's field equations. One of the spun-up solutions has quasilocal mass but no global mass. It has an ergosphere but no event horizon. The angular momentum is constant everywhere beyond the ergosphere. The energy–momentum content of this solution can be interpreted as a rotating string fluid.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/49214/2/cqg4_23_015.pd