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

Asymptotic dynamics in 3D gravity with torsion

We study the nature of boundary dynamics in the teleparallel 3D gravity. The asymptotic field equations with anti-de Sitter boundary conditions yield only two non-trivial boundary modes, related to a conformal field theory with classical central charge. After showing that the teleparallel gravity can be formulated as a Chern-Simons theory, we identify dynamical structure at the boundary as the Liouville theory.Comment: 16 pages, RevTeX, no figure

Generalized Lagrangian of N = 1 supergravity and its canonical constraints with the real Ashtekar variable

We generalize the Lagrangian of N = 1 supergravity (SUGRA) by using an arbitrary parameter $\xi$, which corresponds to the inverse of Barbero's parameter $\beta$. This generalized Lagrangian involves the chiral one as a special case of the value $\xi = \pm i$. We show that the generalized Lagrangian gives the canonical formulation of N = 1 SUGRA with the real Ashtekar variable after the 3+1 decomposition of spacetime. This canonical formulation is also derived from those of the usual N = 1 SUGRA by performing Barbero's type canonical transformation with an arbitrary parameter $\beta (=\xi^{-1})$. We give some comments on the canonical formulation of the theory.Comment: 17 pages, LATE

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

Lessons of spin and torsion: Reply to ``Consistent coupling to Dirac fields in teleparallelism"

In reply to the criticism made by Mielke in the pereceding Comment [Phys. Rev. D69 (2004) 128501] on our recent paper, we once again explicitly demonstrate the inconsistency of the coupling of a Dirac field to gravitation in the teleparallel equivalent of general relativity. Moreover, we stress that the mentioned inconsistency is generic for {\it all} sources with spin and is by no means restricted to the Dirac field. In this sense the $SL(4,R)$-covariant generalization of the spinor fields in the teleparallel gravity theory is irrelevant to the inconsistency problem.Comment: Revtex, 4 pages, no figure

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

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

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

Black hole entropy from the boundary conformal structure in 3D gravity with torsion

Asymptotic symmetry of the Euclidean 3D gravity with torsion is described by two independent Virasoro algebras with different central charges. Elements of this boundary conformal structure are combined with Cardy's formula to calculate the black hole entropy.Comment: LaTeX, 12 pages; v2: one appendix added, typos corrected, minor changes of the tex

Shear-free rotating inflation

We demonstrate the existence of shear-free cosmological models with rotation and expansion which support the inflationary scenarios. The corresponding metrics belong to the family of spatially homogeneous models with the geometry of the closed universe (Bianchi type IX). We show that the global vorticity does not prevent the inflation and even can accelerate it.Comment: Revtex, 12 pages; to appear in Phys. Rev.