Physical interpretation of Newman-Janis rotating systems. I. A unique family of Kerr-Schild systems

The Newman-Janis algorithm and its generalizations can be used mathematically to generate rotating solutions from nonrotating spherically-symmetric solutions within general relativity. The energy-momentum tensors of these solutions 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 a series of two papers, we compare the structure of the eigenvalues and eigenvectors of the rotating and nonrotating energy-momentum tensors (their Segre types) and look for the existence of equations of state relating the energy density and the principal pressures. Part I covers Kerr-Schild systems, Part II more general systems. We find that there is a unique family of stationary axisymmetric Kerr-Schild systems that obey the same equation of state in both the rotating and nonrotating configurations. This family includes the Kerr and Kerr-Newman black holes, as well as rotating spacetimes whose mass function in the nonrotating limit contains a constrained superposition of a cloud of strings term, a Reissner-Nordstrom term, a cosmological constant term, and a Schwarzschild term. We describe the common equation of state relating energy density and pressure in this family of spacetimes and discuss some of its properties.