3.3 Radial Part of the Perturbation
3.4 Computing the Scalar Field Along the Source World Line
3.5 Solutions of the Radial Homogeneous Equation
3.5.1 Heun Confluent (Exact) Solutions
3.5.2 PN Solutions
3.5.3 MST or Hypergeometric-Like Solutions
3.6 Analytical Versus Numerical Results
4 So Far So Good: A List of SF Accomplishments
5 Concluding Remarks
References
Geometry and Analysis in Black Hole Spacetimes
Contents
1 Introduction
2 Background
2.1 Minkowski Space
2.2 Lorentzian Geometry and Causality
2.3 Conventions and Notation

2.4 Einstein Equation
2.5 The Cauchy Problem
2.6 Asymptotically Flat Data
2.7 Komar Integrals
3 Black Holes
3.1 The Schwarzschild Solution
3.1.1 Orbiting Null Geodesics
3.2 Black Hole Stability
3.3 The Kerr Metric
4 Spin Geometry
4.1 Spinors on Minkowski Space
4.2 Spinors on Spacetime
4.3 Fundamental Operators
4.4 Massless Spin-s Fields
4.5 Killing Spinors
4.6 Algebraically Special Spacetimes
4.6.1 Petrov Type D
4.7 Spacetimes Admitting a Killing Spinor
4.8 GHP Formalism
5 The Kerr Spacetime
5.1 Characterizations of Kerr

6 Monotonicity and Dispersion
6.1 Monotonicity for Null Geodesics
6.2 Dispersive Estimates for Fields
7 Symmetry Operators
7.1 Symmetry Operators for the Kerr Wave Equation
8 Outlook
8.1 Teukolsky
8.2 Stability for Linearized Gravity on Kerr
8.3 Nonlinear Stability for Schwarzschild
8.4 Nonlinear Stability for Kerr
References
Study of Fundamental Laws with Antimatter
Contents
1 Introduction
2 Testing CPT
3 Testing the Weak Equivalence Principle
4 Anti-hydrogen at CERN
4.1 Confinement
4.2 Anti-hydrogen Beams