Randall-Sundrum Zero Mode as a Penrose Limit

A generalization of the limiting procedure of Penrose, which allows non-zero cosmological constants and takes into account metrics that contain homogeneous functions of degree zero, is presented. It is shown that any spacetime which admits a spacelike conformal Killing vector has a limit which is conformal to plane waves. If the spacetime is an Einstein space, its limit exists only if the cosmological constant is negative or zero. When the conformal Killing vector is hypersurface orthogonal, the limits of Einstein spacetimes are certain AdS plane waves. In this case the nonlinear version of the Randall-Sundrum zero mode is obtained as the limit of the brane world scenarios.Comment: 8 pages,LaTe

Non-Abelian pp-waves in D=4 supergravity theories

The non-Abelian plane waves, first found in flat spacetime by Coleman and subsequently generalized to give pp-waves in Einstein-Yang-Mills theory, are shown to be 1/2 supersymmetric solutions of a wide variety of N=1 supergravity theories coupled to scalar and vector multiplets, including the theory of SU(2) Yang-Mills coupled to an axion \sigma and dilaton \phi recently obtained as the reduction to four-dimensions of the six-dimensional Salam-Sezgin model. In this latter case they provide the most general supersymmetric solution. Passing to the Riemannian formulation of this theory we show that the most general supersymmetric solution may be constructed starting from a self-dual Yang-Mills connection on a self-dual metric and solving a Poisson equation for e^\phi. We also present the generalization of these solutions to non-Abelian AdS pp-waves which allow a negative cosmological constant and preserve 1/4 of supersymmetry.Comment: Latex, 1+12 page

3-Branes and Uniqueness of the Salam-Sezgin Vacuum

We prove the uniqueness of the supersymmetric Salam-Sezgin (Minkowski)_4\times S^2 ground state among all nonsingular solutions with a four-dimensional Poincare, de Sitter or anti-de Sitter symmetry. We construct the most general solutions with an axial symmetry in the two-dimensional internal space, and show that included amongst these is a family that is non-singular away from a conical defect at one pole of a distorted 2-sphere. These solutions admit the interpretation of 3-branes with negative tension.Comment: Latex, 12 pages; typos corrected, discussion of brane tensions amende

Higher-dimensional resolution of dilatonic black hole singularities

We show that the four-dimensional extreme dilaton black hole with dilaton coupling constant $a= \sqrt{p/(p+2)}$ can be interpreted as a {\it completely non-singular}, non-dilatonic, black $p$-brane in $(4+p)$ dimensions provided that $p$ is {\it odd}. Similar results are obtained for multi-black holes and dilatonic extended objects in higher spacetime dimensions. The non-singular black $p$-brane solutions include the self-dual three brane of ten-dimensional N=2B supergravity and a multi-fivebrane solution of eleven-dimensional supergravity. In the case of a supersymmetric non-dilatonic $p$-brane solution of a supergravity theory, we show that it saturates a bound on the energy per unit $p$-volume.Comment: 27 pages, R/94/28, UCSBTH-94-35 (Comments added to the discussion section

Plane Wave Limits and T-Duality

The Penrose limit is generalized to show that, any leading order solution of the low-energy field equations in any one of the five string theories has a plane wave solution as a limit. This limiting procedure takes into account all the massless fields that may arise and commutes with the T-duality so that any dual solution has again a plane wave limit. The scaling rules used in the limit are unique and stem from the scaling property of the D=11 supergravity action. Although the leading order solutions need not be exact or supersymmetric, their plane wave limits always preserve some portion of the Poincare supersymmetry and solve the relevant field equations in all powers of the string tension parameter. Further properties of the limiting procedure are discussed.Comment: 12 pages, to appear in Physics Letters

Intersecting branes and Supersymmetry

We consider intersecting M-brane solutions of supergravity in eleven dimensions. Supersymmetry turns out to be a powerful tool in obtaining such solutions and their generalizations.Comment: 6 pages, Latex, Presented at Supersymmetry and Quantum Field Theory, International Seminar dedicated to the memory of D. V. Volkov, Kharkov, 199

Screening Model of Magnetotransport Hysteresis Observed in Bilayer Quantum Hall Systems

We report on theoretical and experimental investigations of a novel hysteresis effect that has been observed on the magnetoresistance of quantum-Hall bilayer systems. Extending to these system a recent approach, based on the Thomas-Fermi-Poisson nonlinear screening theory and a local conductivity model, we are able to explain the hysteresis as being due to screening effects such as the formation of ``incompressible strips'', which hinder the electron density in a layer within the quantum Hall regime to reach its equilibrium distribution.Comment: 9 pages, 4 figures, to appear in Physica

Kaluza-Klein electrically charged black branes in M-theory

We present a class of Kaluza-Klein electrically charged black p-brane solutions of ten-dimensional, type IIA superstring theory. Uplifting to eleven dimensions these solutions are studied in the context of M-theory. They can be interpreted either as a p+1 extended object trapped around the eleventh dimension along which momentum is flowing or as a boost of the following backgrounds: the Schwarzschild black (p+1)-brane or the product of the (10-p)-dimensional Euclidean Schwarzschild manifold with the (p+1)-dimensional Minkowski spacetime.Comment: 16 pages, uses latex and epsf macro, figures include

Stringy Robinson-Trautman Solutions

A class of solutions of the low energy string theory in four dimensions is studied. This class admits a geodesic, shear-free null congruence which is non-twisting but in general diverging and the corresponding solutions in Einstein's theory form the Robinson-Trautman family together with a subset of the Kundt's class. The Robinson-Trautman conditions are found to be frame invariant in string theory. The Lorentz Chern-Simons three form of the stringy Robinson-Trautman solutions is shown to be always closed. The stringy generalizations of the vacuum Robinson-Trautman equation are obtained and three subclasses of solutions are identified. One of these subclasses exists, among all the dilatonic theories, only in Einstein's theory and in string theory. Several known solutions including the dilatonic black holes, the pp- waves, the stringy C-metric and certain solutions which correspond to exact conformal field theories are shown to be particular members of the stringy Robinson-Trautman family. Some new solutions which are static or asymptotically flat and radiating are also presented. The radiating solutions have a positive Bondi mass. One of these radiating solutions has the property that it settles down smoothly to a black hole state at late retarded times.Comment: Latex, 30 Pages, 1 Figure; to appear in Phys. Rev.

Self-consistent local-equilibrium model for density profile and distribution of dissipative currents in a Hall bar under strong magnetic fields

Recent spatially resolved measurements of the electrostatic-potential variation across a Hall bar in strong magnetic fields, which revealed a clear correlation between current-carrying strips and incompressible strips expected near the edges of the Hall bar, cannot be understood on the basis of existing equilibrium theories. To explain these experiments, we generalize the Thomas-Fermi--Poisson approach for the self-consistent calculation of electrostatic potential and electron density in {\em total} thermal equilibrium to a {\em local equilibrium} theory that allows to treat finite gradients of the electrochemical potential as driving forces of currents in the presence of dissipation. A conventional conductivity model with small values of the longitudinal conductivity for integer values of the (local) Landau-level filling factor shows that, in apparent agreement with experiment, the current density is localized near incompressible strips, whose location and width in turn depend on the applied current.Comment: 9 pages, 7 figure