Teleparallelism: A New Insight Into Gravity

Teleparallel gravity, a gauge theory for the translation group, turns up as fully equivalent to Einstein's general relativity. In spite of this equivalence, it provides a whole new insight into gravitation. It breaks several paradigms related to the geometric approach of general relativity, and introduces new concepts in the description of the gravitational interaction. The purpose of this chapter is to explore some of these concepts, as well as discuss possible consequences for gravitation, mainly those that could be relevant for the quantization of the gravitational field.Comment: Chapter to appear in "Handbook of Spacetime", edited by A. Ashtekar and V. Petcov (Springer, Berlin, 2013). V2: misprints corrected, references update

Lorentz Connections and Gravitation

The different roles played by Lorentz connections in general relativity and in teleparallel gravity are reviewed. Some of the consequences of this difference are discussed.Comment: Lecture presented at the Sixth International School on Field Theory and Gravity, Petropolis, Brazil, 201

Active and passive fields face to face

The statistical properties of active and passive scalar fields transported by the same turbulent flow are investigated. Four examples of active scalar have been considered: temperature in thermal convection, magnetic potential in two-dimensional magnetohydrodynamics, vorticity in two-dimensional Ekman turbulence and potential temperature in surface flows. In the cases of temperature and vorticity, it is found that the active scalar behavior is akin to that of its co-evolving passive counterpart. The two other cases indicate that this similarity is in fact not generic and differences between passive and active fields can be striking: in two-dimensional magnetohydrodynamics the magnetic potential performs an inverse cascade while the passive scalar cascades toward the small-scales; in surface flows, albeit both perform a direct cascade, the potential temperature and the passive scalar have different scaling laws already at the level of low-order statistical objects. These dramatic differences are rooted in the correlations between the active scalar input and the particle trajectories. The role of such correlations in the issue of universality in active scalar transport and the behavior of dissipative anomalies is addressed.Comment: 36 pages, 20 eps figures, for the published version see http://www.iop.org/EJ/abstract/1367-2630/6/1/07