The quadratic spinor Lagrangian is equivalent to the teleparallel theory

The quadratic spinor Lagrangian is shown to be equivalent to the teleparallel / tetrad representation of Einstein's theory. An important consequence is that the energy-momentum density obtained from this quadratic spinor Lagrangian is essentially the same as the ``tensor'' proposed by Moller in 1961.Comment: 10 pages, RevTe

Symmetric Hyperbolic System in the Self-dual Teleparallel Gravity

In order to discuss the well-posed initial value formulation of the teleparallel gravity and apply it to numerical relativity a symmetric hyperbolic system in the self-dual teleparallel gravity which is equivalent to the Ashtekar formulation is posed. This system is different from the ones in other works by that the reality condition of the spatial metric is included in the symmetric hyperbolicity and then is no longer an independent condition. In addition the constraint equations of this system are rather simpler than the ones in other works.Comment: 8 pages, no figure

Gravitational Energy of Kerr and Kerr Anti-de Sitter Space-times in the Teleparallel Geometry

In the context of the Hamiltonian formulation of the teleparallel equivalent of general relativity we compute the gravitational energy of Kerr and Kerr Anti-de Sitter (Kerr-AdS) space-times. The present calculation is carried out by means of an expression for the energy of the gravitational field that naturally arises from the integral form of the constraint equations of the formalism. In each case, the energy is exactly computed for finite and arbitrary spacelike two-spheres, without any restriction on the metric parameters. In particular, we evaluate the energy at the outer event horizon of the black holes.Comment: 11 pages, 1 figure, to appear in JHEP11(2003)00

Cartan's spiral staircase in physics and, in particular, in the gauge theory of dislocations

In 1922, Cartan introduced in differential geometry, besides the Riemannian curvature, the new concept of torsion. He visualized a homogeneous and isotropic distribution of torsion in three dimensions (3d) by the "helical staircase", which he constructed by starting from a 3d Euclidean space and by defining a new connection via helical motions. We describe this geometric procedure in detail and define the corresponding connection and the torsion. The interdisciplinary nature of this subject is already evident from Cartan's discussion, since he argued - but never proved - that the helical staircase should correspond to a continuum with constant pressure and constant internal torque. We discuss where in physics the helical staircase is realized: (i) In the continuum mechanics of Cosserat media, (ii) in (fairly speculative) 3d theories of gravity, namely a) in 3d Einstein-Cartan gravity - this is Cartan's case of constant pressure and constant intrinsic torque - and b) in 3d Poincare gauge theory with the Mielke-Baekler Lagrangian, and, eventually, (iii) in the gauge field theory of dislocations of Lazar et al., as we prove for the first time by arranging a suitable distribution of screw dislocations. Our main emphasis is on the discussion of dislocation field theory.Comment: 31 pages, 8 figure

Avoiding degenerate coframes in an affine gauge approach to quantum gravity

In quantum models of gravity, it is surmized that configurations with degenerate coframes could occur during topology change of the underlying spacetime structure. However, the coframe is not the true Yang--Mills type gauge field of the translations, since it lacks the inhomogeneous gradient term in the gauge transformations. By explicitly restoring this ``hidden" piece within the framework of the affine gauge approach to gravity, one can avoid the metric or coframe degeneracy which would otherwise interfere with the integrations within the path integral. This is an important advantage for quantization.Comment: 14 pages, Preprint Cologne-thp-1993-H

Teleparallel Gravity and Dimensional Reductions of Noncommutative Gauge Theory

We study dimensional reductions of noncommutative electrodynamics on flat space which lead to gauge theories of gravitation. For a general class of such reductions, we show that the noncommutative gauge fields naturally yield a Weitzenbock geometry on spacetime and that the induced diffeomorphism invariant field theory can be made equivalent to a teleparallel formulation of gravity which macroscopically describes general relativity. The Planck length is determined in this setting by the Yang-Mills coupling constant and the noncommutativity scale. The effective field theory can also contain higher-curvature and non-local terms which are characteristic of string theory. Some applications to D-brane dynamics and generalizations to include the coupling of ordinary Yang-Mills theory to gravity are also described.Comment: 31 pages LaTeX; References adde

A global pH sensor: Agrobacterium sensor protein ChvG regulates acid-inducible genes on its two chromosomes and Ti plasmid

10.1073/pnas.192439499Proceedings of the National Academy of Sciences of the United States of America991912369-12374PNAS