Breaking Generalized Covariance, Classical Renormalization and Boundary Conditions from Superpotentials

Superpotentials offer a direct means of calculating conserved charges associated with the asymptotic symmetries of space-time. Yet superpotentials have been plagued with inconsistencies, resulting in nonphysical or incongruent values for the mass, angular momentum and energy loss due to radiation. The approach of Regge and Teitelboim, aimed at a clear Hamiltonian formulation with a boundary, and its extension to the Lagrangian formulation by Julia and Silva have resolved these issues, and have resulted in a consistent, well-defined and unique variational equation for the superpotential, thereby placing it on a firm footing. A hallmark solution of this equation is the KBL superpotential obtained from the first-order Lovelock Lagrangian. Nevertheless, here we show that these formulations are still insufficient for Lovelock Lagrangians of higher orders. We present a paradox, whereby the choice of fields affects the superpotential for equivalent on-shell dynamics. We offer two solutions to this paradox: either the original Lagrangian must be effectively renormalized, or that boundary conditions must be imposed, so that space-time be asymptotically maximally symmetric. Non-metricity is central to this paradox, and we show how quadratic non-metricity in the bulk of space-time contributes to the conserved charges on the boundary, where it vanishes identically. This is a realization of the gravitational Higgs mechanism, proposed by Percacci, where the non-metricity is the analogue of the Goldstone boson.Comment: review format, 44 page

A Puff of Steem: Security Analysis of Decentralized Content Curation

Decentralized content curation is the process through which uploaded posts are ranked and filtered based exclusively on users\u27 feedback. Platforms such as the blockchain-based Steemit employ this type of curation while providing monetary incentives to promote the visibility of high quality posts according to the perception of the participants. Despite the wide adoption of the platform very little is known regarding its performance and resilience characteristics. In this work, we provide a formal model for decentralized content curation that identifies salient complexity and game-theoretic measures of performance and resilience to selfish participants. Armed with our model, we provide a first analysis of Steemit identifying the conditions under which the system can be expected to correctly converge to curation while we demonstrate its susceptibility to selfish participant behaviour. We validate our theoretical results with system simulations in various scenarios