Symmetries of the Einstein Equations

Generalized symmetries of the Einstein equations are infinitesimal transformations of the spacetime metric that formally map solutions of the Einstein equations to other solutions. The infinitesimal generators of these symmetries are assumed to be local, \ie at a given spacetime point they are functions of the metric and an arbitrary but finite number of derivatives of the metric at the point. We classify all generalized symmetries of the vacuum Einstein equations in four spacetime dimensions and find that the only generalized symmetry transformations consist of: (i) constant scalings of the metric (ii) the infinitesimal action of generalized spacetime diffeomorphisms. Our results rule out a large class of possible ``observables'' for the gravitational field, and suggest that the vacuum Einstein equations are not integrable.Comment: 15 pages, FTG-114-USU, Plain Te

New Symbolic Tools for Differential Geometry, Gravitation, and Field Theory

DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the variational calculus. These capabilities, combined with dramatic recent improvements in symbolic approaches to solving algebraic and differential equations, have allowed for development of powerful new tools for solving research problems in gravitation and field theory. The purpose of this paper is to describe some of these new tools and present some advanced applications involving: Killing vector fields and isometry groups, Killing tensors and other tensorial invariants, algebraic classification of curvature, and symmetry reduction of field equations.Comment: 42 page

The origins of the Acheulean: past and present perspectives on a major transition in human evolution

The emergence of the Acheulean from the earlier Oldowan constitutes a major transition in human evolution, the theme of this special issue. This paper discusses the evidence for the origins of the Acheulean, a cornerstone in the history of human technology, from two perspectives; firstly, a review of the history of investigations on Acheulean research is presented. This approach introduces the evolution of theories throughout the development of the discipline, and reviews the way in which cumulative knowledge led to the prevalent explanatory framework for the emergence of the Acheulean. The second part presents the current state of the art in Acheulean origins research, and reviews the hard evidence for the appearance of this technology in Africa around 1.7 Ma, and its significance for the evolutionary history of Homo erectus. This article is part of the themed issue ‘Major transitions in human evolution’

Video augmentation to support video-based learning

Multimedia content and video-based learning are expected to take a central role in the post-pandemic world. Thus, providing new advanced interfaces and services that further exploit their potential becomes of paramount importance. A challenging area deals with developing intelligent visual interfaces that integrate the knowledge extracted from multimedia materials into educational applications. In this respect, we designed a web-based video player that is aimed to support video consumption by exploiting the knowledge extracted from the video in terms of concepts explained in the video and prerequisite relations between them. This knowledge is used to augment the video lesson through visual feedback methods. Specifically, in this paper we investigate the use of two types of visual feedback, i.e. an augmented transcript and a dynamic concept map (map of concept's flow), to improve video comprehension in the first-watch learning context. Our preliminary findings suggest that both the methods help the learner to focus on the relevant concepts and their related contents. The augmented transcript has an higher impact on immediate comprehension compared to the map of concepts' flow, even though the latter is expected to be more powerful to support other tasks such as exploration and in-depth analysis of the concepts in the video

No New Symmetries of the Vacuum Einstein Equations

In this note we examine some recently proposed solutions of the linearized vacuum Einstein equations. We show that such solutions are {\it not} symmetries of the Einstein equations, because of a crucial integrability condition.Comment: 9 pages, Te

A 6 kV–150 A, 8 ns rise time pulse generator for excitation of ferroelectric cathodes

A pulse generator with the following characteristics is presented: the voltage ranges in the interval 0.1–6 kV, the maximum delivered current is 150 A, the pulse length ranges within the interval 100–300 ns, the rise time and the decay times are, respectively, 10 and 25 ns on 50 Ω resistive load and the repetition rate is higher than 1 MHz. The circuit has a source capacitor of 10 nF charged at the needed voltage, the capacitor feeds the load through a parallel of two fast and high voltage solid state switches. The nanosecond rise time and the square fashion of the pulse have been accomplished arranging all the components in cylindrical symmetry. A bipolar pulse is obtained coupling two circuits with opposite polarity