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

TL;DR

This paper applies a complex coordinate transformation to derive a rotating metric from a static Einstein-Born-Infeld solution, revealing limitations of the Newman-Janis algorithm for non-linear electromagnetic sources.

Contribution

It demonstrates that the Newman-Janis algorithm does not produce physically consistent rotating solutions for Einstein-Born-Infeld black holes.

Findings

The new metric behaves like a rotating charged source.

The energy-momentum tensor does not match that of a rotating Born-Infeld monopole.

The complex transformation's interpretation is limited to linear sources.

Abstract

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.