Unique characterization of the Bel-Robinson tensor

We prove that a completely symmetric and trace-free rank-4 tensor is, up to sign, a Bel-Robinson type tensor, i.e., the superenergy tensor of a tensor with the same algebraic symmetries as the Weyl tensor, if and only if it satisfies a certain quadratic identity. This may be seen as the first Rainich theory result for rank-4 tensors.Comment: extended version, 13 pages, shorter version published in Class.Quant.Gra

Algebraic Rainich theory and antisymmetrisation in higher dimensions

The classical Rainich(-Misner-Wheeler) theory gives necessary and sufficient conditions on an energy-momentum tensor $T$ to be that of a Maxwell field (a 2-form) in four dimensions. Via Einstein's equations these conditions can be expressed in terms of the Ricci tensor, thus providing conditions on a spacetime geometry for it to be an Einstein-Maxwell spacetime. One of the conditions is that $T^2$ is proportional to the metric, and it has previously been shown in arbitrary dimension that any tensor satisfying this condition is a superenergy tensor of a simple $p$-form. Here we examine algebraic Rainich conditions for general $p$-forms in higher dimensions and their relations to identities by antisymmetrisation. Using antisymmetrisation techniques we find new identities for superenergy tensors of these general (non-simple) forms, and we also prove in some cases the converse; that the identities are sufficient to determine the form. As an example we obtain the complete generalisation of the classical Rainich theory to five dimensions.Comment: 16 pages, LaTe

Conserved Matter Superenergy Currents for Orthogonally Transitive Abelian G2 Isometry Groups

In a previous paper we showed that the electromagnetic superenergy tensor, the Chevreton tensor, gives rise to a conserved current when there is a hypersurface orthogonal Killing vector present. In addition, the current is proportional to the Killing vector. The aim of this paper is to extend this result to the case when we have a two-parameter Abelian isometry group that acts orthogonally transitive on non-null surfaces. It is shown that for four-dimensional Einstein-Maxwell theory with a source-free electromagnetic field, the corresponding superenergy currents lie in the orbits of the group and are conserved. A similar result is also shown to hold for the trace of the Chevreton tensor and for the Bach tensor, and also in Einstein-Klein-Gordon theory for the superenergy of the scalar field. This links up well with the fact that the Bel tensor has these properties and the possibility of constructing conserved mixed currents between the gravitational field and the matter fields.Comment: 15 page

Two dimensional Sen connections and quasi-local energy-momentum

The recently constructed two dimensional Sen connection is applied in the problem of quasi-local energy-momentum in general relativity. First it is shown that, because of one of the two 2 dimensional Sen--Witten identities, Penrose's quasi-local charge integral can be expressed as a Nester--Witten integral.Then, to find the appropriate spinor propagation laws to the Nester--Witten integral, all the possible first order linear differential operators that can be constructed only from the irreducible chiral parts of the Sen operator alone are determined and examined. It is only the holomorphy or anti-holomorphy operator that can define acceptable propagation laws. The 2 dimensional Sen connection thus naturally defines a quasi-local energy-momentum, which is precisely that of Dougan and Mason. Then provided the dominant energy condition holds and the 2-sphere S is convex we show that the next statements are equivalent: i. the quasi-local mass (energy-momentum) associated with S is zero; ii.the Cauchy development $D(\Sigma)$ is a pp-wave geometry with pure radiation ($D(\Sigma)$ is flat), where $\Sigma$ is a spacelike hypersurface whose boundary is S; iii. there exist a Sen--constant spinor field (two spinor fields) on S. Thus the pp-wave Cauchy developments can be characterized by the geometry of a two rather than a three dimensional submanifold.Comment: 20 pages, Plain Tex, I

Algebraic Rainich conditions for the tensor V

Algebraic conditions on the Ricci tensor in the Rainich-Misner-Wheeler unified field theory are known as the Rainich conditions. Penrose and more recently Bergqvist and Lankinen made an analogy from the Ricci tensor to the Bel-Robinson tensor $B_{\alpha\beta\mu\nu}$, a certain fourth rank tensor quadratic in the Weyl curvature, which also satisfies algebraic Rainich-like conditions. However, we found that not only does the tensor $B_{\alpha\beta\mu\nu}$ fulfill these conditions, but so also does our recently proposed tensor $V_{\alpha\beta\mu\nu}$, which has many of the desirable properties of $B_{\alpha\beta\mu\nu}$. For the quasilocal small sphere limit restriction, we found that there are only two fourth rank tensors $B_{\alpha\beta\mu\nu}$ and $V_{\alpha\beta\mu\nu}$ which form a basis for good energy expressions. Both of them have the completely trace free and causal properties, these two form necessary and sufficient conditions. Surprisingly either completely traceless or causal is enough to fulfill the algebraic Rainich conditions. Furthermore, relaxing the quasilocal restriction and considering the general fourth rank tensor, we found two remarkable results: (i) without any symmetry requirement, the algebraic Rainich conditions only require totally trace free; (ii) with a symmetry requirement, we recovered the same result as in the quasilocal small sphere limit.Comment: 17 page

The Chevreton Tensor and Einstein-Maxwell Spacetimes Conformal to Einstein Spaces

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 Petrov types \textbf{N} or \textbf{O}. We prove that the trace of the Chevreton tensor is related to the Bach tensor and use this to find all Einstein-Maxwell spacetimes with a zero cosmological constant that have a vanishing Bach tensor. Among these spacetimes we then look for those which are conformal to Einstein spaces. We find that the electromagnetic field and the Weyl tensor must be aligned, and in the case that the electromagnetic field is null, the spacetime must be conformally Ricci-flat and all such solutions are known. In the non-null case, since the general solution is not known on closed form, we settle with giving the integrability conditions in the general case, but we do give new explicit examples of Einstein-Maxwell spacetimes that are conformal to Einstein spaces, and we also find examples where the vanishing of the Bach tensor does not imply that the spacetime is conformal to a $C$-space. The non-aligned Einstein-Maxwell spacetimes with vanishing Bach tensor are conformally $C$-spaces, but none of them are conformal to Einstein spaces.Comment: 22 pages. Corrected equation (12

Iatrogenic Vascular Injuries in Sweden. A Nationwide Study 1987–2005

ObjectivesTo study the epidemiology of vascular injuries, with special focus on Iatrogenic Vascular Injuries (IVIs) and time-trends.Design and methodsFrom the Swedish national vascular registry, Swedvasc, prospectively registered data on vascular injuries during 1987–2005 were analysed and cross-referenced for mortalityagainst the population registry.ResultsOf 1853 injuries, 48% were caused by iatrogenic, 29% penetrating and 23% blunt trauma. In the three groups median age was 68, 35 and 40 years, respectively. The annual incidence of procedures for vascular injuries increased from 1.2–1.6 per 100 000 inhabitants and the proportion of IVIs increased from 41 to 51%, during the period. Mortality was higher after IVI (4.9%) compared to non-IVI (2.5%). Patients with IVI also had more co-morbidities; 58% cardiac disease, 44% hypertension, and 18% renal dysfunction.Among 888 IVIs, right femoral arterial injury was the most frequent (37%). The most common vascular reconstruction was direct suture (39%) followed by by-pass or interposition graft (19%, of which prosthetics were used in over half the cases). Endovascular repair increased from 4.6% to 15% between 1987 and 2005.ConclusionsVascular injuries, in particular iatrogenic ones, appear to be increasing. Iatrogenic injuries affect vulnerable patients with co-morbidities and are associated with a high mortality

The impact of an upstream buyer consolidation and downstream intermodal rail-based solution on logistics cost in the China-Europe container trades

Author's accepted version (postprint).This is an Accepted Manuscript of an article published by Elsevier in Case Studies on Transport Policy on 19/03/2020.Available online: https://www.sciencedirect.com/science/article/pii/S2213624X19300884?via%3DihubIn the typical structure of the supply chains associated with the Asia-Europe container trade, containers are stuffed in China, and the cargo is subsequently cross-docked at a major European logistics hub or a distribution centre closer to the customer for further distribution to the final retailing points. However, this solution may not be optimal in the perspective of total logistics cost. Upstream buyer consolidation at the origin and a downstream rail-based intermodal system at the destination has been regarded as a potential solution for reducing the costs of supply chains. The purpose of this study is to identify the benefits of this potential solution. This research is based on a case study obtained from a Swedish retailer with a chain of retailing points in Scandinavia and Poland. A comparative analysis is used to reveal the cost advantage of the alternative solution. Our findings suggest that this alternative solution may reduce monetary logistics cost from two aspects: converting LCL shipments to FCL shipments and converting almost full 20-foot FCL shipments to 40-foot FCL shipments. In addition, certain non-monetary benefits of buyer consolidation, including reduced possibility of delay, reduced complexity, reduced carbon emissions and reduced activities in the destination countries, are illustrated in this paper. Based on our calculation, the cost-saving potential of the new alternative solution illustrated in this case study is considerable, which suggests that such solutions might be desirable as an alternative to the typical arrangements in this trade. Keywords: Upstream buyer consolidation; Rail-based intermodal system; Asia-Europe container supply chains; Monetary benefits; Non-monetary benefits.acceptedVersio

Another positivity proof and gravitational energy localizations

Two locally positive expressions for the gravitational Hamiltonian, one using 4-spinors the other special orthonormal frames, are reviewed. A new quadratic 3-spinor-curvature identity is used to obtain another positive expression for the Hamiltonian and thereby a localization of gravitational energy and positive energy proof. These new results provide a link between the other two methods. Localization and prospects for quasi-localization are discussed.Comment: 14 pages REVTe