Dilaton Black Holes with Electric Charge

Static spherically symmetric solutions of the Einstein-Maxwell gravity with the dilaton field are described. The solutions correspond to black holes and are generalizations of the previously known dilaton black hole solution. In addition to mass and electric charge these solutions are labeled by a new parameter, the dilaton charge of the black hole. Different effects of the dilaton charge on the geometry of space-time of such black holes are studied. It is shown that in most cases the scalar curvature is divergent at the horizons. Another feature of the dilaton black hole is that there is a finite interval of values of electric charge for which no black hole can exist.Comment: 20 pages, LaTeX file + 1 figure, CALT-68-1885. (the postscript file is improved

Dynamical Compactification, Standard Cosmology and the Accelerating Universe

A cosmological model based on Kaluza-Klein theory is studied. A metric, in which the scale factor of the compact space evolves as an inverse power of the radius of the observable universe, is constructed. The Freedmann-Robertson-Walker equations of standard four-dimensional cosmology are obtained precisely. The pressure in our universe is an effective pressure expressed in terms of the components of the higher dimensional energy-momentum tensor. In particular, this effective pressure could be negative and might therefore explain the acceleration of our present universe. A special feature of this model is that, for a suitable choice of the parameters of the metric, the higher dimensional gravitational coupling constant could be negative.Comment: 11 pages, uses revte

New Charged Dilaton Solutions in 2+1 Dimensions and Solutions with Cylindrical Symmetry in 3+1 Dimensions

We report a new family of solutions to Einstein-Maxwell-dilaton gravity in 2+1 dimensions and Einstein-Maxwell gravity with cylindrical symmetry in 3+1 dimensions. A set of static charged solutions in 2+1 dimensions are obtained by a compactification of charged solutions in 3+1 dimensions with cylindrical symmetry. These solutions contain naked singularities for certain values of the parameters considered. New rotating charged solutions in 2+1 dimensions and 3+1 dimensions are generated treating the static charged solutions as seed metrics and performing $SL(2;R)$ transformations.Comment: Latex. No figure

Conformal Covariantization of Moyal-Lax Operators

A covariant approach to the conformal property associated with Moyal-Lax operators is given. By identifying the conformal covariance with the second Gelfand-Dickey flow, we covariantize Moyal-Lax operators to construct the primary fields of one-parameter deformation of classical $W$-algebras.Comment: 13 pages, Revtex, no figures, v.2: typos corrected, references added and conclusion modifie

Entropy for Asymptotically AdS_3 Black Holes

We propose that Strominger's method to derive the BTZ black hole entropy is in fact applicable to other asymptotically AdS_3 black holes and gives the correct functional form of entropies. We discuss various solutions in the Einstein-Maxwell theory, dilaton gravity, Einstein-scalar theories, and Einstein-Maxwell-dilaton theory. In some cases, solutions approach AdS_3 asymptotically, but their entropies do not have the form of Cardy's formula. However, it turns out that they are actually not "asymptotically $AdS_3$" solutions. On the other hand, for truly asymptotically AdS_3 solutions, their entropies have the form of Cardy's formula. In this sense, all known solutions are consistent with our proposal.Comment: 21 pages, LaTeX; v2: added discussion for section 3.

On the B\"acklund Transformation for the Moyal Korteweg-de Vries Hierarchy

We study the B\"acklund symmetry for the Moyal Korteweg-de Vries (KdV) hierarchy based on the Kuperschmidt-Wilson Theorem associated with second Gelfand-Dickey structure with respect to the Moyal bracket, which generalizes the result of Adler for the ordinary KdV.Comment: 9 pages, Revte

General analysis of self-dual solutions for the Einstein-Maxwell-Chern-Simons theory in (1+2) dimensions

The solutions of the Einstein-Maxwell-Chern-Simons theory are studied in (1+2) dimensions with the self-duality condition imposed on the Maxwell field. We give a closed form of the general solution which is determined by a single function having the physical meaning of the quasilocal angular momentum of the solution. This function completely determines the geometry of spacetime, also providing the direct computation of the conserved total mass and angular momentum of the configurations.Comment: 3 pages, REVTEX file, no figure

Rotating Dilaton Solutions in 2+1 Dimensions

We report a three parameter family of solutions for dilaton gravity in 2+1 dimensions with finite mass and finite angular momentum. These solutions are obtained by a compactification of vacuum solutions in 3+1 dimensions with cylindrical symmetry. One class of solutions corresponds to conical singularities and the other leads to curvature singularities.Comment: Accepted to be published in Gen. Rel. Grav., added reference

No Black Hole Theorem in Three-Dimensional Gravity

A common property of known black hole solutions in (2+1)-dimensional gravity is that they require a negative cosmological constant. In this letter, it is shown that a (2+1)-dimensional gravity theory which satisfies the dominant energy condition forbids the existence of a black hole to explain the above situation.Comment: 3 pages, no figures, to be published in Physical Review Letter

Supersymmetric Moyal-Lax Representations

The super Moyal-Lax representation and the super Moyal momentum algebra are introduced and the properties of simple and extended supersymmetric integrable models are systematically investigated. It is shown that, much like in the bosonic cases, the super Moyal-Lax equation can be interpreted as a Hamiltonian equation and can be derived from an action. Similarly, we show that the parameter of non-commutativity, in this case, is related to the central charge of the second Hamiltonian structure of the system. The super Moyal-Lax description allows us to go to the dispersionless limit of these models in a singular limit and we discuss some of the properties of such systems.Comment: 16 page