Exact Lagrangian submanifolds in simply-connected cotangent bundles

We consider exact Lagrangian submanifolds in cotangent bundles. Under certain additional restrictions (triviality of the fundamental group of the cotangent bundle, and of the Maslov class and second Stiefel-Whitney class of the Lagrangian submanifold) we prove such submanifolds are Floer-cohomologically indistinguishable from the zero-section. This implies strong restrictions on their topology. An essentially equivalent result was recently proved independently by Nadler, using a different approach.Comment: 28 pages, 3 figures. Version 2 -- derivation and discussion of the spectral sequence considerably expanded. Other minor change

Gravitational waves from black hole collisions via an eclectic approach

We present the first results in a new program intended to make the best use of all available technologies to provide an effective understanding of waves from inspiralling black hole binaries in time for imminent observations. In particular, we address the problem of combining the close-limit approximation describing ringing black holes and full numerical relativity, required for essentially nonlinear interactions. We demonstrate the effectiveness of our approach using general methods for a model problem, the head-on collision of black holes. Our method allows a more direct physical understanding of these collisions indicating clearly when non-linear methods are important. The success of this method supports our expectation that this unified approach will be able to provide astrophysically relevant results for black hole binaries in time to assist gravitational wave observations.Comment: 4 pages, 3 eps figures, Revte

New Formalism for Numerical Relativity

We present a new formulation of the Einstein equations that casts them in an explicitly first order, flux-conservative, hyperbolic form. We show that this now can be done for a wide class of time slicing conditions, including maximal slicing, making it potentially very useful for numerical relativity. This development permits the application to the Einstein equations of advanced numerical methods developed to solve the fluid dynamic equations, {\em without} overly restricting the time slicing, for the first time. The full set of characteristic fields and speeds is explicitly given.Comment: uucompresed PS file. 4 pages including 1 figure. Revised version adds a figure showing a comparison between the standard ADM approach and the new formulation. Also available at http://jean-luc.ncsa.uiuc.edu/Papers/ Appeared in Physical Review Letters 75, 600 (1995

The Electronic States of Two Oppositely doped Mott Insulators Bilayers

We study the effect of Coulomb interaction between two oppositely doped low-dimensional tJ model systems. We exactly show that, in the one-dimensional case, an arbitrarily weak interaction leads to the formation of charge neutral electron-hole pairs. We then use two different mean-field theories to address the two-dimensional case, where inter-layer excitons also form and condense. We propose that this results in new features which have no analog in single layers, such as the emergence of an insulating spin liquid phase. Our simple bilayer model might have relevance to the physics of doped Mott insulator interfaces and of the new four layer Ba2CaCu4O8 compound.Comment: 4 pages, 1 figur