Classical and Quantum Waves on Black Hole Backgrounds P Blue Max Planck Glom D Häfner Bordeaux
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Titles and Abstracts Courses Classical and Quantum Waves on Black Hole Backgrounds P. Blue (Max Planck Glom), D. Häfner (Bordeaux), J. P. Nicolas (Brest) and S. De Bièvre (Lille) In this course, three aspects of black hole physics will be discussed: two concern classical waves, namely superradiance (J.P. Nicolas and S. De Bièvre) and local decay and stability (P. Blue), whereas the third one, the Hawking effect (D. Häfner) is of quantum nature. It arises when a star collapses to a (rotating) black hole. The courses will be on the upper graduate or post-doctoral level and, to be enjoyed, will require no more than the basic notions of (pseudo) Riemannian geometry, a certain familiarity with quantum mechanics, a taste for analysis, and a definite passion for mathematical physics. Lecture 1 Particle superradiance (J. P. Nicolas) 90' 1.1 Introduction to the Kerr black hole metric 1.2 The geodesics of the Kerr black hole 1.3 The Penrose mecanism for “particle” superradiance, or how to extract energy from a black hole Lecture 2 The Hawking effect for beginners (D. Häfner) 90' 2.1 A simple example: the moving mirror 2.2 A model for black hole formation through star collapse 2.3 The classical Dirac equation on the Kerr metric Lecture 3 Decay for Maxwell's equation outside a Schwarzschild black hole.
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- open classical
- black hole
- local decay
- nonrelativistic quantum
- quantum particle
- exchange interactions
- major open
- limit
- charges up
Titles and Abstracts
Courses Classical and Quantum Waves on Black Hole Backgrounds P. Blue (Max Planck Glom), D. Hfner (Bordeaux), J. P. Nicolas (Brest) and S. De BiÈvre (Lille) In this course, three aspects of black hole physics will be discussed:two concern classical waves, namely superradiance (J.P. Nicolas and S. De BiÈvre) and local decay and stability (P. Blue), whereas the third one, the Hawking effect (D. Hfner) is of quantum nature.It arises when a star collapses to a (rotating) black hole. The courses will be on the upper graduate or post-doctoral level and, to be enjoyed, will require no more than the basic notions of (pseudo) Riemannian geometry, a certain familiarity with quantum mechanics, a taste for analysis, and a definite passion for mathematical physics. Lecture 1 Particle superradiance (J. P. Nicolas)90’ 1.1 Introduction to the Kerr black hole metric 1.2 The geodesics of the Kerr black hole 1.3 The Penrose mecanism for “particle” superradiance, or how to extract energy from a black hole
Lecture 2 The Hawking effect for beginners (D. Hfner)90’ 2.1 A simple example:the moving mirror 2.2 A model for black hole formation through star collapse 2.3 The classical Dirac equation on the Kerr metric
Lecture 3Decay for Maxwell’s equation outside a Schwarzschild black hole. (Pieter Blue)50’ The Maxwell-Einstein system describes the classical theory of electromagnetism and gravity.A black hole is a class of solutions with a particular type of coherent structure. Thereis a three-parameter family of known, static, exact solutions. The parameters are mass, charge, and angular momentum.The Schwarzschild solution is the solution with zero charge and angular momentum.It is expected that all perturbations of black hole solutions will asymptotically approach one of the known solutions.This stability result is a major open problem in math-ematical relativity.Even the proof of the stability of empty space was a very challenging problem.One can imagine thinking of this is a classical open system, with the black-hole parameters evolving under the influence of electromagnetic and gravitational radiation.In this talk, I will describe recent work on decay for the decoupled Maxwell field on a fixed Schwarzschild background.This prob-lem can be thought of as a model problem for the full problem, and the recent work builds on previous work for the wave equation.The vector field method is used to prove pointwise decay estimates.The Schwarzschild background has or-
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