SL(2,R)SL(2,R) symmetry and quasi-normal modes in the BTZ black hole

With the help of two new intrinsic tensor fields associated with the $SL(2,R)$ quadratic Casimir of Killing fields, we uncover the $SL(2,R)$ symmetry satisfied by the solutions to the equations of motion for various fields in the BTZ black hole in a uniform way by performing tensor and spinor analysis without resorting to any specific coordinate system. Then with the standard algebraic method developed recently, we determine the quasi-normal modes for various fields in the BTZ black hole. As a result, the quasi-normal modes are given by the infinite tower of descendants of the chiral highest weight mode, which is in good agreement with the previous analytic result obtained by exactly solving equations of motion instead.Comment: JHEP style, 1+13 pages, version to appear in JHE

A Riemann-Hilbert Problem for an Energy Dependent Schr\"odinger Operator

\We consider an inverse scattering problem for Schr\"odinger operators with energy dependent potentials. The inverse problem is formulated as a Riemann-Hilbert problem on a Riemann surface. A vanishing lemma is proved for two distinct symmetry classes. As an application we prove global existence theorems for the two distinct systems of partial differential equations $u_t+(u^2/2+w)_x=0, w_t\pm u_{xxx}+(uw)_x=0$ for suitably restricted, complementary classes of initial data

(2,2)-Formalism of General Relativity: An Exact Solution

I discuss the (2,2)-formalism of general relativity based on the (2,2)-fibration of a generic 4-dimensional spacetime of the Lorentzian signature. In this formalism general relativity is describable as a Yang-Mills gauge theory defined on the (1+1)-dimensional base manifold, whose local gauge symmetry is the group of the diffeomorphisms of the 2-dimensional fibre manifold. After presenting the Einstein's field equations in this formalism, I solve them for spherically symmetric case to obtain the Schwarzschild solution. Then I discuss possible applications of this formalism.Comment: 2 figures included, IOP style file neede

On the Weyl transverse frames in type I spacetimes

We apply a covariant and generic procedure to obtain explicit expressions of the transverse frames that a type I spacetime admits in terms of an arbitrary initial frame. We also present a simple and general algorithm to obtain the Weyl scalars $\Psi_2^T$, $\Psi_0^T$ and $\Psi_4^T$ associated with these transverse frames. In both cases it is only necessary to choose a particular root of a cubic expression.Comment: 12 pages, submitted to Gen. Rel. Grav. (6-3-2004

A note on the uniqueness of global static decompositions

We discuss when static Killing vector fields are standard, that is, leading to a global orthogonal splitting of the spacetime. We prove that such an orthogonal splitting is unique whenever the natural space is compact. This is carried out by proving that many notable spacelike submanifolds must be contained in an orthogonal slice. Possible obstructions to the global splitting are also considered.Comment: 6 pages, no figure

Cosmological Perturbations of Quantum-Mechanical Origin and Anisotropy of the Microwave Background

Cosmological perturbations generated quantum-mechanically (as a particular case, during inflation) possess statistical properties of squeezed quantum states. The power spectra of the perturbations are modulated and the angular distribution of the produced temperature fluctuations of the CMBR is quite specific. An exact formula is derived for the angular correlation function of the temperature fluctuations caused by squeezed gravitational waves. The predicted angular pattern can, in principle, be revealed by the COBE-type observations.Comment: 9 pages, WUGRAV-92-17 Accepted for Publication in Phys. Rev. Letters (1993

Cosmic Microwave Background Dipole induced by double inflation

The observed CMBR dipole is generally interpreted as the consequence of the peculiar motion of the Sun with respect to the reference frame of the CMBR. This article proposes an alternative interpretation in which the observed dipole is the result of isocurvature perturbations on scales larger than the present Hubble radius. These perturbations are produced in the simplest model of double inflation, depending on three parameters. The observed dipole and quadrupole can be explained in this model, while severely constraining its parameters.Comment: Latex, 9 pages, no figure, to appear in Phys. Rev.

Contractionary Devaluation, and Dynamic Adjustment of Exports and Wages

Recent macroeconomic models of developing countries have emphasized the possibility of contactionary devaluations, stressing that domestic aggregate demand is likely to be reduced by the devaluations while aggregate supply may respond only slowly to the change in relative prices brought about by the devaluation. These results have been obtained in static models. In this paper we add wage and export-sector dynamics to the models of contractionary devaluation, and show that the effects which produce contractionary devaluations in the short term can produce limit cycles in the long run. The economy never returns to long-run equilibrium following a devaluation, but rather moves with fixed periodicity through successive phases of boom and bust