Related papers: Purely magnetic spacetimes
It is shown that there are no vacuum space-times (with or without cosmological constant) for which the Weyl-tensor is purely gravito-magnetic with respect to a normal and timelike congruence of observers.
Purely magnetic spacetimes, in which the Riemann tensor satisfies $R_{abcd}u^bu^d=0$ for some unit timelike vector $u^a$, are studied. The algebraic consequences for the Weyl and Ricci tensors are examined in detail and consideration given…
It is shown that there are no vacuum space-times (with or without cosmological constant) for which the Weyl-tensor is purely gravito-magnetic with respect to a congruence of freely falling observers.
We consider time reversal transformations to obtain twofold orthogonal splittings of any tensor on a Lorentzian space of arbitrary dimension n. Applied to the Weyl tensor of a spacetime, this leads to a definition of its electric and…
In a paper by Maartens, Lesame and Ellis (Class. Quant. Grav. 15, 1005) it was shown that irrotational dust solutions with vanishing electric part of the Weyl tensor are subject to severe integrability conditions and it was conjectured that…
Einstein spacetimes (that is vacuum spacetimes possibly with a non-zero cosmological constant {\Lambda}) with constant non-zero Weyl eigenvalus are considered. For type Petrov II & D this assumption allows one to prove that the non-repeated…
The electric and the magnetic part of the Weyl tensor, as well as the invariants obtained from them, are calculated for the Bondi vacuum metric. One of the invariants vanishes identically and the other only exhibits contributions from terms…
We show that there are no vacuum solutions with a purely magnetic Weyl tensor with respect to an observer submitted to kinematic restrictions involving first order differential scalars. This result generalizes previous ones for the…
Recent results on purely electric (PE) or magnetic (PM) spacetimes in n dimensions are summarized. These include: Weyl types; diagonalizability; conditions under which direct (or warped) products are PE/PM.
We give a classification of the type D spacetimes based on the invariant differential properties of the Weyl principal structure. Our classification is established using tensorial invariants of the Weyl tensor and, consequently, besides its…
A four-index tensor is constructed with terms both quadratic in the Riemann tensor and linear in its second derivatives, which has zero divergence for space-times with vanishing scalar curvature. This tensor reduces in vacuum to the…
We obtain expressions for the shear and the vorticity tensors of perfect-fluid spacetimes, in terms of the divergence of the Weyl tensor. For such spacetimes, we prove that if the gradient of the energy density is parallel to the velocity,…
A theorem related to the Newman-Penrose constants is proven. The theorem states that all the Newman-Penrose constants of asymptotically flat, stationary, asymptotically algebraically special electrovacuum spacetimes are zero.…
All spacetimes for an irrotational collisionless fluid with a purely electric Weyl tensor, with spacetime curvature determined by the exact Einstein field equations, are shown to be integrable. These solutions include the relativistic…
We study umbilically synchronized space-times $M$ that have vanishing electric part of the Weyl tensor and show that (i) If $dim(M) = 4$, then $M$ is conformally flat, (ii) If $dim(M) > 4$, $M$ is conformally flat if and only if the spatial…
We have solved the Einstein-Maxwell equations for a class of isotropic metrics with constant spatial curvature in the presence of magnetic fields. We consider a slight modification of the Tolman averaging relations so that the…
In this paper we characterize the source-free Einstein-Maxwell spacetimes which have a trace-free Chevreton tensor. We show that this is equivalent to the Chevreton tensor being of pure-radiation type and that it restricts the spacetimes to…
We analyze the spacetimes admitting a direction for which the relative electric and magnetic Weyl fields are aligned. We give an invariant characterization of these metrics and study the properties of its Debever null vectors. The…
We study the class of vacuum (Ricci flat) six-dimensional spacetimes admitting a non-degenerate multiple Weyl aligned null direction l, thus being of Weyl type II or more special. Subject to an additional assumption on the asymptotic…
We examine the effect that the magnetic part of the Weyl tensor has on the large-scale expansion of space. This is done within the context of a class of cosmological models that contain regularly arranged discrete masses, rather than a…