Complete classification of purely magnetic, non-rotating and non-accelerating perfect fluids

Abstract

Recently the class of purely magnetic non-rotating dust spacetimes has been shown to be empty (Wylleman, Class. Quant. Grav. 23, 2727). It turns out that purely magnetic rotating dust models are subject to severe integrability conditions as well. One of the consequences of the present paper is that also rotating dust cannot be purely magnetic when it is of Petrov type D or when it has a vanishing spatial gradient of the energy density. For purely magnetic and non-rotating perfect fluids on the other hand, which have been fully classified earlier for Petrov type D (Lozanovski, Class. Quant. Grav. 19, 6377), the fluid is shown to be non-accelerating if and only if the spatial density gradient vanishes. Under these conditions, a new and algebraically general solution is found, which is unique up to a constant rescaling, which is spatially homogeneous of Bianchi type $V{I}_0$, has degenerate shear and is of Petrov type I($M^{\infty })$ in the extended Arianrhod-McIntosh classification. The metric and the equation of state are explicitly constructed and properties of the model are briefly discussed. We finally situate it within the class of normal geodesic flows with degenerate shear tensor.

arXiv comment12 pages; introduction partly rewritten, notation made more clear, table of results added

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• Refinements of the Weyl tensor classification in five dimensions
• Gravitomagnetic Accelerators
• Stationary cylindrical anisotropic fluid and new purely magnetic GR solutions
• Gravitomagnetism in the Lewis cylindrical metrics
• Gravitomagnetism and the significance of the curvature scalar invariants
• Poynting vector, super-Poynting vector, and principal observers in electromagnetism and general relativity
• Purely radiative perfect fluids
• On the flow of perfect energy tensors
• Observer-based invariants for cosmological models