Newman-Janis Ansatz in conformastatic spacetimes

TL;DR

This paper explores the application of the Newman-Janis Ansatz to conformastatic spacetimes, revealing its limitations and showing that it generally produces non-vacuum solutions with matter content, especially when starting from Schwarzschild spacetime.

Contribution

It demonstrates that the Newman-Janis Ansatz can be applied to conformastatic vacuum metrics but often results in non-vacuum, matter-filled solutions, highlighting its limitations.

Findings

The Ansatz can be applied to conformastatic vacuum metrics.

Resulting solutions often describe relativistic fluids, not vacuum.

Application depends on the seed solution's representation.

Abstract

The Newman-Janis Ansatz was used first to obtain the stationary Kerr metric from the static Schwarzschild metric. Many works have been devoted to investigate the physical significance of this Ansatz, but no definite answer has been given so far. We show that this Ansatz can be applied in general to conformastatic vacuum metrics, and leads to stationary generalizations which, however, do not preserve the conformal symmetry. We investigate also the particular case when the seed solution is given by the Schwarzschild spacetime and show that the resulting rotating configuration does not correspond to a vacuum solution, even in the limiting case of slow rotation. In fact, it describes in general a relativistic fluid with anisotropic pressure and heat flux. This implies that the Newman-Janis Ansatz strongly depends on the choice of representation for the seed solution. We interpret this result as as a further indication of its applicability limitations.