Notes on black holes and three dimensional gravity

These notes are the written version of two lectures delivered at the VIII Mexican School on Particles and Fields on November 1998. The level of the notes is basic assuming only some knowledge on Statistical Mechanics, General Relativity and Yang-Mills theory. After a brief introduction to the classical and semiclassical aspects of black holes, we review some relevant results on 2+1 quantum gravity. These include the Chern-Simons formulation and its affine Kac-Moody algebra, the asymptotic algebra of Brown and Henneaux, and the statistical mechanics description of 2+1 black holes. Hopefully, this contribution will be complementary with the review paper hep-th/9901148 by the same author, and perhaps, a shortcut to some recent developments in three dimensional gravity.Comment: 20 pages. Uses aipproc. To appear in the proceedings of the VIII Mexican School on Particles and Field

A Cross-Country Analysis of the Risk Factors for Depression at the Micro and Macro Level

Past research has provided evidence of the role of some personal characteristics as risk factors for depression. However, few studies have examined jointly their specific impact and whether country characteristics change the probability of being depressed. In general, this is due to the use of single-country databases. The aim of this paper is to extend previous findings by employing a much larger dataset and including the country effects mentioned above. The paper estimates probit models with country effects and explores linkages between specific environmental factors and depression using data from the 2007 Gallup Public Opinion Poll. Findings indicate that depression is positively related to being a woman, adulthood, divorce, widowhood, unemployment and low income. Moreover, there is evidence of the significant positive association between inequality and depression, especially for those living in urban areas. Finally, some population’s characteristics facilitate depression (age distribution and religious affiliation).Depression, Health, Well-being, Cross-country research

Three-dimensional quantum geometry and black holes

We review some aspects of three-dimensional quantum gravity with emphasis in the `CFT -> Geometry' map that follows from the Brown-Henneaux conformal algebra. The general solution to the classical equations of motion with anti-de Sitter boundary conditions is displayed. This solution is parametrized by two functions which become Virasoro operators after quantisation. A map from the space of states to the space of classical solutions is exhibited. Some recent proposals to understand the Bekenstein-Hawking entropy are reviewed in this context. The origin of the boundary degrees of freedom arising in 2+1 gravity is analysed in detail using a Hamiltonian Chern-Simons formalism.Comment: 39 pages, Latex, no figures. Invited talk at the Second Meeting "Trends in Theoretical Physics", held in Buenos Aires, December, 1998. v2: References added and minor corrections. v3: An incorrect statement about the sign of the Chern-Simons level erased. Extended (and in some cases modified) discussions in most sections. References adde

Collisional dynamics of multiple dark solitons in a toroidal Bose–Einstein condensate: quasiparticle picture

Abstract: We study the collisional dynamics of multiple dark solitons in a Bose–Einstein condensate confined by a toroidal trap. We assume a tight enough confinement in the radial direction to prevent possible dissipative effects due to the presence of solitonic vortices. Analytical expressions for the initial order parameters with imprinted phases are utilized to generate different initial arrays of solitons, for which the time-dependent Gross–Pitaevskii equation is numerically solved. Given that the soliton velocity is conserved due to the lack of dissipation, we are able to apply a simple quasiparticle description of the soliton dynamics. In fact, the trajectory equations are written in terms of the velocities and the angular shifts produced at each collision, in analogy to the infinite one-dimensional system. To calculate the angular shifts, we directly extract them from the trajectories given by the Gross–Pitaevskii simulations and, on the other hand, we show that accurate values can be analytically obtained by adapting a formula valid for the infinite one-dimensional system that involves the healing length, which in our inhomogeneous system must be evaluated in terms of the sound velocity along the azimuthal direction. We further show that very good estimates of such a sound velocity can be directly determined by using the ground state density profile and the values of the imprinted phases. We discuss the possible implementation of the system here proposed using the current experimental techniques.Fil: Cataldo, Horacio Maximo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Jezek, Dora Marta. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentin