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

Abstract

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.

arXiv commentReplaced with updated version, published at Phys. Rev. D 104, 124066 (2021)

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• Rotating anisotropic stringy spheroid in a modified Hartle formalism
• Compact regular objects from an electrified Tolman-like density: A new interior region for the Kerr-Newman spacetime
• Geometric properties of slowly rotating black holes embedded in matter environments
• Axisymmetric generalization of zero-scalar-curvature solutions from the Schwarzschild metric via the Newman-Janis algorithm
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• Slowly rotating covariant anisotropic objects
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• Newman-Janis Algorithm from Taub-NUT Instantons
• An obstruction and residual-completion theory for Newman--Janis deformations