The Volume of the Past Light-Cone and the Paneitz Operator

We study a conjecture involving the invariant volume of the past light-cone from an arbitrary observation point back to a fixed initial value surface. The conjecture is that a 4th order differential operator which occurs in the theory of conformal anomalies gives $8\pi$ when acted upon the invariant volume of the past light-cone. We show that an extended version of the conjecture is valid for an arbitrary homogeneous and isotropic geometry. First order perturbation theory about flat spacetime reveals a violation of the conjecture which, however, vanishes for any vacuum solution of the Einstein equation. These results may be significant for constructing quantum gravitational observables, for quantifying the back-reaction on spacetime expansion and for alternate gravity models which feature a timelike vector field.Comment: 22 pages, no figures, 5 tables. Version 2 substantially extended to cover nonzero spatial curvature, and with simplified derivation

Rescaling the local: multi-academy trusts, private monopoly and statecraft in England

For the past six years successive UK governments in England have introduced reforms intended to usher in less aggregated, top-down, bureaucratically overloaded models of service delivery as well as secure conditions for greater school autonomy. Yet the ‘hollowing out’ of local government has not resulted in less bureaucracy on the ground or less regulation from above, nor has it diminished hierarchy as an organising principle of education governance. In some cases, monopolies and monopolistic practices dominated by powerful bureaucracies and professional groups persist, albeit realised through the involvement of new actors and organisations from business and philanthropy. In this paper I adopt a governmentality perspective to explore the political significance of large multi-academy trusts (MATs) – private sponsors contracted by central government to run publicly funded schools – to the generation of new scalar hierarchies and accountability infrastructures that assist in bringing the gaze of government to bear upon the actions of schools that are otherwise less visible under local government management. On this account, it is argued, MATs are integral to statecraft and the invention and assemblage of particular apparatuses for intervening upon specific organisations, spaces and peoples