Physical interpretation of Newman-Janis rotating systems. II. General systems

TL;DR

This paper extends the analysis of rotating spacetimes generated by the Newman-Janis algorithm, revealing diverse Segre types and significant changes in energy-momentum tensor structures during rotation, with implications for understanding their physical nature.

Contribution

It generalizes previous work to include all static spherically symmetric solutions, analyzing the eigenvalue structures and equations of state of the resulting rotating systems.

Findings

Rotating systems exhibit almost all Segre types except [31] and [(31)].

The Segre type can change drastically from nonrotating to rotating configurations.

Conditions are identified for the existence of multiple equations of state in these systems.

Abstract

Drake and Szekeres have extended the Newman-Janis algorithm to produce stationary axisymmetric spacetimes from general static spherically symmetric solutions of the Einstein equations. The algorithm mathematically generates an energy-momentum tensor for the rotating solution, but the rotating and nonrotating system may or may not represent the same physical system, in the sense of both being a perfect fluid, or an electromagnetic field, or a $\Lambda$-term, and so on. In Part I (arxiv:2104.02255), we compared the structure of the eigenvalues and eigenvectors of the rotating and nonrotating energy-momentum tensors (their Segre types) and looked for the existence of equations of state relating the rotating energy density and principal pressures for Kerr-Schild systems. Here we extend our analysis to general static spherically symmetric systems obtained according to the Drake-Szekeres generalization of the Newman-Janis algorithm. We find that these rotating systems can have almost all Segre types except [31] and [(31)]. Moreover, the Segre type of the spacetime can change severely in passing from the nonrotating to the rotating configurations, for example to $[11Z\bar{Z}]$ from seed systems which were initially [(111,1)]. We also find conditions dictating how many equations of state may exist in a Drake-Szekeres system.