Norbert Van den Bergh

Complete classification of purely magnetic, nonrotating, nonaccelerating perfect fluids

Recently the class of purely magnetic nonrotating dust spacetimes has been shown to be empty [L. Wylleman, Classical Quantum Gravity 23, 2727 (2006).]. 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 nonrotating perfect fluids on the other hand, which have been fully classified earlier for Petrov type D [C. Lozanovski, Classical Quantum Gravity 19, 6377 (2002).], the fluid is shown to be nonaccelerating 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 VI{sub 0}, has degenerate shear, and is of Petrov type I(M{sup {infinity}}) 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.

Purely gravito-magnetic vacuum spacetimes

It is shown that there are no vacuum spacetimes (with or without cosmological constant) for which the Weyl tensor is purely gravito-magnetic with respect to a normal and timelike congruence of observers.

Tidal effects cannot be absent in a vacuum

It is shown that there are no vacuum spacetimes (with or without cosmological constant) for which the Weyl-tensor is purely gravito-magnetic with respect to a congruence of freely falling observers.

Silent universes with a cosmological constant

We study non-degenerate (Petrov type I) silent universes in the presence of a non-vanishing cosmological constant Λ. In contrast to the Λ = 0 case, for which the orthogonally spatially homogeneous Bianchi type I metrics most likely are the only admissible metrics, solutions are shown to exist when Λ > 0. The general solution is presented for the case where one of the eigenvalues of the expansion tensor is 0.

Shear-free perfect fluids with a solenoidal electric curvature

We prove that the vorticity or the expansion vanishes for any shear-free perfect fluid solution of the Einstein field equations where the pressure satisfies a barotropic equation of state and the spatial divergence of the electric part of the Weyl tensor is zero.

Petrov type I silent universes with G3 isometry group: the uniqueness result recovered

Irrotational dust spacetimes with vanishing magnetic Weyl curvature are called silent universes (Matarrese et al 1994 Phys. Rev. D 72 320). The silent universe conjecture (Sopuerta 1997 Phys. Rev. D 55 5936, van Elst et al 1997 Class. Quantum Grav. 14 1151) states that the only algebraically general silent universes are the orthogonally spatially homogeneous Bianchi I models. In the same paper by Sopuerta, this was confirmed for the subcase where the spacetime also admits a group G3 of isometries. However, the proof contains a conceptual mistake. We recover the result in a different way.

Petrov type D pure radiation fields of Kundt’s class

We present all Petrov type D pure radiation space-times, with or without cosmological constant, with a shear-free, nondiverging geodesic principal null congruence. We thus completely solve the problem of aligned Petrov type D pure radiation fields: either these are Robinson–Trautman space-times and are all explicitly known or they belong to the Kundt family, for which so far only isolated examples existed in the literature.

An exhaustive classification of aligned petrov type D purely magnetic perfect fluids

We prove that aligned Petrov type D purely magnetic perfect fluids are necessarily locally rotationally symmetric and hence are all explicitly known.

Classification results on purely electric or magnetic perfect fluids

Non-conformally flat, non-vacuum perfect fluid models for which the magnetic, resp. electric, part of the Weyl tensor w.r.t. the fluid congruence vanishes, are called purely electric (PE), resp. purely magnetic (PM), perfect fluids. Their Petrov type is necessarily I or D. They are of particular interest, since the electric part is the relativistic generalization of the tidal tensor in Newtonian theory, whereas the magnetic part has no Newtonian analogue. A survey of recent classification results is presented, with focus on Petrov type D and on the Petrov type I non-accelerating subclass. Important known universe models are naturally embedded in the analysis, while new and physically interesting PE and PM families emerge.

SILENT UNIVERSES WITH A POSITIVE COSMOLOGICAL CONSTANT

The existence of inhomogeneous and algebraically general silent universes with a positive cosmological constant is demonstrated and explicit solutions are given when one of the eigenvalues of the expansion tensor is 0.