Curvature operators and scalar curvature invariants

We continue the study of the question of when a pseudo-Riemannain manifold can be locally characterised by its scalar polynomial curvature invariants (constructed from the Riemann tensor and its covariant derivatives). We make further use of alignment theory and the bivector form of the Weyl operator in higher dimensions, and introduce the important notions of diagonalisability and (complex) analytic metric extension. We show that if there exists an analytic metric extension of an arbitrary dimensional space of any signature to a Riemannian space (of Euclidean signature), then that space is characterised by its scalar curvature invariants. In particular, we discuss the Lorentzian case and the neutral signature case in four dimensions in more detail.Comment: 26 pages, 2 figure

Pseudo-Riemannian VSI spaces

In this paper we consider pseudo-Riemannian spaces of arbitrary signature for which all of their polynomial curvature invariants vanish (VSI spaces). We discuss an algebraic classification of pseudo-Riemannian spaces in terms of the boost weight decomposition and define the ${\bf S}_i$- and ${\bf N}$-properties, and show that if the curvature tensors of the space possess the ${\bf N}$-property then it is a VSI space. We then use this result to construct a set of metrics that are VSI. All of the VSI spaces constructed possess a geodesic, expansion-free, shear-free, and twist-free null-congruence. We also discuss the related Walker metrics.Comment: 14 page

Lorentzian manifolds and scalar curvature invariants

We discuss (arbitrary-dimensional) Lorentzian manifolds and the scalar polynomial curvature invariants constructed from the Riemann tensor and its covariant derivatives. Recently, we have shown that in four dimensions a Lorentzian spacetime metric is either $\mathcal{I}$-non-degenerate, and hence locally characterized by its scalar polynomial curvature invariants, or is a degenerate Kundt spacetime. We present a number of results that generalize these results to higher dimensions and discuss their consequences and potential physical applications.Comment: submitted to CQ

A spacetime not characterised by its invariants is of aligned type II

By using invariant theory we show that a (higher-dimensional) Lorentzian metric that is not characterised by its invariants must be of aligned type II; i.e., there exists a frame such that all the curvature tensors are simultaneously of type II. This implies, using the boost-weight decomposition, that for such a metric there exists a frame such that all positive boost-weight components are zero. Indeed, we show a more general result, namely that any set of tensors which is not characterised by its invariants, must be of aligned type II. This result enables us to prove a number of related results, among them the algebraic VSI conjecture.Comment: 14pages, CQG to appea

Brane Waves

In brane-world cosmology gravitational waves can propagate in the higher dimensions (i.e., in the `bulk'). In some appropriate regimes the bulk gravitational waves may be approximated by plane waves. We systematically study five-dimensional gravitational waves that are algebraically special and of type N. In the most physically relevant case the projected non-local stress tensor on the brane is formally equivalent to the energy-momentum tensor of a null fluid. Some exact solutions are studied to illustrate the features of these branes; in particular, we show explicity that any plane wave brane can be embedded into a 5-dimensional Siklos spacetime. More importantly, it is possible that in some appropriate regime the bulk can be approximated by gravitational plane waves and thus may act as initial conditions for the gravitational field in the bulk (thereby enabling the field equations to be integrated on the brane).Comment: 9 pages v3:revised version, to appear in CQ

Minutes of the Society for Ontofabulatory Research: report from the Committee for Aeronautical Psychogeography

In late 2012, the RAF’s Remotely Piloted Aircraft Squadron began operating their provision of armed Reaper drones from Waddington air base in Lincolnshire. In a world in which military affairs have been revolutionized, and conflicts integrated as normalized states of crisis, the ‘drone’ is an expression of a system of power continually boosted by the myths and fears entangled in its paradoxical operation. Lincolnshire, known locally as ‘bomber county’, and defined by the narratives and aesthetics of its military culture, acts as microcosm for debates over the new spatialities of such power. Here we address these debates in reference to an experimental film project which creatively deploys McKenzie Wark’s concept of ‘telesthesia’, exploiting ‘perception at a distance’ as a tool for what Nicholas Mirzoeff calls ‘countervisuality’. Inspired by avant-garde games of the twentieth century, the film maps and newly imagines the media-ecological battlefield in which we find ourselves. In briefly perceiving our collective presence as both HERE and THERE, we aim to invoke what the novelist China Miéville calls a ‘swillage of...awe and horror from ‘beyond’, back into the everyday’, a weirding affect which the conventional narratives of our county will fail to contain or explain

After the aftermath

Siegfried Zielinski. […After the Media] News from the Slow-Fading Twentieth Century. Trans. Gloria Custance. Univocal, 2013. 276 pp. Media theory has a problem with the new. The new is an obstacle, it is obsolete, it is yesterday’s news. Of the many responses to a late 20th century obsession with “new media,” current attempts to rethink the dominant historical narrative of media culture best encapsulate the problem. This disruptive set of methods and approaches has come to be known as media archaeology (Huhtamo and Parikka 2011). For figures associated with the emergent field, such as the German theorist Siegfried Zielinski, conventional histories of media are too selective, too closely aligned to a restrictive linear progression from past to present. For Zielinski, the unquestioned authority of this narrative produces a problem with the term media itself. Media becomes aligned to the spectacle of progress, synonymous with the bright universal future (Zielinski 2006: 32). In […After the Media] News from the Slow-Fading Twentieth Century, Zielinski employs archaeological methods to reexamine media after the future. As he makes clear from the outset, this is not motivated by paradigmatic posturing but by the urgent need to redeem media criticism at a time of crisis