A trick for passing degenerate points in Ashtekar formulation

We examine one of the advantages of Ashtekar's formulation of general relativity: a tractability of degenerate points from the point of view of following the dynamics of classical spacetime. Assuming that all dynamical variables are finite, we conclude that an essential trick for such a continuous evolution is in complexifying variables. In order to restrict the complex region locally, we propose some `reality recovering' conditions on spacetime. Using a degenerate solution derived by pull-back technique, and integrating the dynamical equations numerically, we show that this idea works in an actual dynamical problem. We also discuss some features of these applications.Comment: 9 pages by RevTeX or 16 pages by LaTeX, 3 eps figures and epsf-style file are include

Topological 2-form Gravity in Four Dimensions

A kind of topological field theory is proposed as a candidate to describe the global structure of the 2-form Einstein gravity with or without a cosmological constant. Indeed in the former case, we show that a quantum state in the candidate gives an exact solution of the Wheeler-DeWitt equation. The BRST quantization based on the Batalin-Fradkin-Vilkovisky (BFV) formalism is carried out for this topological version of the 2-form Einstein gravity.Comment: 15 page

Local virial relation for self-gravitating system

We demonstrate that the quasi-equilibrium state in self-gravitating $N$-body system after cold collapse are uniquely characterized by the local virial relation using numerical simulations. Conversely assuming the constant local virial ratio and Jeans equation for spherically steady state system, we investigate the full solution space of the problem under the constant anisotropy parameter and obtain some relevant solutions. Especially, the local virial relation always provides a solution which has a power law density profile in both the asymptotic regions $r\to 0$ and $\infty$. This type of solutions observed commonly in many numerical simulations. Only the anisotropic velocity dispersion controls this asymptotic behavior of density profile.Comment: 9 pages, 15 eps figures, RevTex, submitted to PR

Gravitational Instantons and Moduli Spaces of Topological 2-form Gravity

A topological version of four-dimensional (Euclidean) Einstein gravity which we propose regards anti-self-dual 2-forms and an anti-self-dual part of the frame connections as fundamental fields. The theory describes the moduli spaces of conformally self-dual Einstein manifolds for the non-zero cosmological constant case and Einstein-Kahlerian manifold with the vanishing real first Chern class for the zero cosmological constant. In the non-zero cosmological constant case, we evaluate the index of the elliptic complex associated with the moduli space and calculate the partition function. We also clarify the moduli space and its dimension for the zero cosmological constant case which are related to the Plebansky's heavenly equations.Comment: 36pages, LaTex, TIT/HEP-247/COSMO-4

Noncommutative Topological Half-flat Gravity

We formulate a noncommutative description of topological half-flat gravity in four dimensions. BRST symmetry of this topological gravity is deformed through a twisting of the usual BRST quantization of noncommutative gauge theories. Finally it is argued that resulting moduli space of instantons is characterized by the solutions of a noncommutative version of the Plebanski's heavenly equation.Comment: 12+1 pages, revtex4, no figure

Half-Metallic Ferrimagnetism in Mn_2VAl

We show that Mn_2VAl is a compound for which the generalized gradient approximation (GGA) to the exchange-correlation functional in density functional theory makes a qualitative change in predicted behavior compared to the usual local density approximation (LDA). Application of GGA leads to prediction of Mn_2VAl being a half-metallic ferrimagnet, with the minority channel being the conducting one. The electronic and magnetic structure is analyzed and contrasted with the isostructural enhanced semimetal Fe_2VAl.Comment: 5 pages, Latex, 6 postscript figures. Description and figures of the (minority) Fermi surfaces have been adde

Symmetries and observables in topological gravity

After a brief review of topological gravity, we present a superspace approach to this theory. This formulation allows us to recover in a natural manner various known results and to gain some insight into the precise relationship between different approaches to topological gravity. Though the main focus of our work is on the vielbein formalism, we also discuss the metric approach and its relationship with the former formalism.Comment: 34 pages; a few explanations added in subsection 2.2.1, published version of pape

Magnetoresistance of antidot lattices with grain boundaries

The magnetotransport properties of antidot lattices containing artificially designed grain boundaries have been measured. We find that the grain boundaries broaden the commensurability resonances and displace them anisotropically. These phenomena are unexpectedly weak but differ characteristically from isotropic, Gaussian disorder in the antidot positions. The observations are interpreted in terms of semiclassical trajectories which tend to localize along the grain boundaries within certain magnetic field intervals. Furthermore, our results indicate how the transport through superlattices generated by self-organizing templates may get influenced by grain boundaries.Comment: 6 pages, 3 figure