Contents

• Introduction
• Preliminary
  • Causal Structure of Spacetimes
    • A Global Structure?
      • The Basic Definitions on Global Structure
    • Causal Structure
      • Domain of Influence
      • Slices
      • Domain of Dependence
  • The Physical Significance of Curvature
    • Raychaudhuri Equation
    • Null Curve
    • Energy Condition
    • Conjugate Points
    • Trapped Surfaces
  • Singularity Theorems
    • About Singularity
    • Singularity Theorems
    • Application to Black Holes
• Main
  • Topological Censorship
    • Physical Meaning of the Theorem
    • The Two Lemmas
    • About the Proof of the Theorem
  • Generalization of the Topological Censorship Theorem
    • Lemma 1
    • De Sitter Universe
    • Asymptotically de Sitter
    • De Sitter outside a Compact set S
  • Primordial Black Holes
    • About Black Hole
    • Constraint on Black Hole in the Universe
• Appendix
  • Topological Censorship: original article
    • Article
    • Extract of the errata
  • Prerequisite
    • Topology of a Manifold
    • Einstein Equation
  • Some Solution of the Einstein Equation
    • Minkowski Spacetime
    • Schwarzschild Spacetime
    • Robertson & Walker Spacetime
    • The de Sitter Spacetime
  • Tools
    • Penrose Diagram
    • GR-Tensor
      • Notations and Commands
      • Input
  • Analogy with Fluid Dynamics
    • Analogy in the notation
    • Hypothesis
    • Equation
  • Volume Expansion in Robertson & Walker
    • Timelike Geodesics
    • Null Geodesics
  • Proof of the Theorem
    • The two Lemma
    • The Theorem
  • Acknowledgment
• List of Figures
• List of Tables
• References
• Index

• Introduction