Lectures on Linear Stability of Rotating Black Holes

These lecture notes are concerned with linear stability of the non-extreme Kerr geometry under perturbations of general spin. After a brief review of the Kerr black hole and its symmetries, we describe these symmetries by Killing fields and work out the connection to conservation laws. The Penrose process and superradiance effects are discussed. Decay results on the long-time behavior of Dirac waves are outlined. It is explained schematically how the Maxwell equations and the equations for linearized gravitational waves can be decoupled to obtain the Teukolsky equation. It is shown how the Teukolsky equation can be fully separated to a system of coupled ordinary differential equations. Linear stability of the non-extreme Kerr black hole is stated as a pointwise decay result for solutions of the Cauchy problem for the Teukolsky equation. The stability proof is outlined, with an emphasis on the underlying ideas and methods.Comment: 25 pages, LaTeX, 3 figures, lectures given at first DOMOSCHOOL in July 2018, minor improvements (published version

High-Tech Tools for Teaching Physics: the Physics Education Technology Project

This article appeared in the Journal of Online Teaching and Learning September 15, 2006.This paper introduces a new suite of computer simulations from the Physics Education Technology (PhET) project, identifies features of these educational tools, and demonstrates their utility. We compare the use of PhET simulations to the use of more traditional educational resources in lecture, laboratory, recitation and informal settings of introductory college physics. In each case we demonstrate that simulations are as productive, or more productive, for developing student conceptual understanding as real equipment, reading resources, or chalk-talk lectures. We further identify six key characteristic features of these simulations that begin to delineate why these are productive tools. The simulations: support an interactive approach, employ dynamic feedback, follow a constructivist approach, provide a creative workplace, make explicit otherwise inaccessible models or phenomena, and constrain students productively

The status of the heavy quark systems

We review various inequalities on the order and the spacing of energy levels, wave function at the origin, etc... which were obtained since 1977 in the framework of the Schrodinger equation and applied to quarkonium and also to muonic atoms and alcaline atoms. We also present a fit of mesons and baryons made of b, c, s quarks and antiquarks, keeping the 1981 parameters and comparing with present experimental data.Comment: 21 pages, 3 figure

Optimal trap shape for a Bose gas with attractive interactions

Dilute Bose gas with attractive interactions is considered at zero temperature, when practically all atoms are in Bose-Einstein condensate. The problem is addressed aiming at answering the question: What is the optimal trap shape allowing for the condensation of the maximal number of atoms with negative scattering lengths? Simple and accurate analytical formulas are derived allowing for an easy analysis of the optimal trap shapes. These analytical formulas are the main result of the paper.Comment: Latex file, 21 page